Properties

Label 9702.2.a
Level $9702$
Weight $2$
Character orbit 9702.a
Rep. character $\chi_{9702}(1,\cdot)$
Character field $\Q$
Dimension $169$
Newform subspaces $107$
Sturm bound $4032$
Trace bound $31$

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Defining parameters

Level: \( N \) \(=\) \( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9702.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 107 \)
Sturm bound: \(4032\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(5\), \(13\), \(17\), \(19\), \(23\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9702))\).

Total New Old
Modular forms 2080 169 1911
Cusp forms 1953 169 1784
Eisenstein series 127 0 127

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(13\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(13\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(11\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(11\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(15\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(14\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(11\)
Plus space\(+\)\(74\)
Minus space\(-\)\(95\)

Trace form

\( 169 q - q^{2} + 169 q^{4} - 2 q^{5} - q^{8} + O(q^{10}) \) \( 169 q - q^{2} + 169 q^{4} - 2 q^{5} - q^{8} - 2 q^{10} + q^{11} - 2 q^{13} + 169 q^{16} - 18 q^{17} - 12 q^{19} - 2 q^{20} - q^{22} - 4 q^{23} + 159 q^{25} - 14 q^{26} + 2 q^{29} - 8 q^{31} - q^{32} - 6 q^{34} + 30 q^{37} - 4 q^{38} - 2 q^{40} + 6 q^{41} + 52 q^{43} + q^{44} + 4 q^{47} - 39 q^{50} - 2 q^{52} - 38 q^{53} - 6 q^{55} - 50 q^{58} + 16 q^{59} - 2 q^{61} - 8 q^{62} + 169 q^{64} - 52 q^{65} + 44 q^{67} - 18 q^{68} - 20 q^{71} + 10 q^{73} - 46 q^{74} - 12 q^{76} + 80 q^{79} - 2 q^{80} - 14 q^{82} - 20 q^{83} - 76 q^{85} + 8 q^{86} - q^{88} - 6 q^{89} - 4 q^{92} + 8 q^{94} + 32 q^{95} - 46 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9702))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7 11
9702.2.a.a 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}-q^{11}+\cdots\)
9702.2.a.b 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}+q^{11}+\cdots\)
9702.2.a.c 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+q^{11}+\cdots\)
9702.2.a.d 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.e 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.f 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.g 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.h 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.i 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.j 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.k 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots\)
9702.2.a.l 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+q^{11}-5q^{13}+q^{16}+\cdots\)
9702.2.a.m 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+q^{11}-2q^{13}+q^{16}+\cdots\)
9702.2.a.n 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+q^{11}-2q^{13}+q^{16}+\cdots\)
9702.2.a.o 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+q^{11}+5q^{13}+q^{16}+\cdots\)
9702.2.a.p 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{11}+\cdots\)
9702.2.a.q 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.r 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.s 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.t 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.u 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.v 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.w 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.x 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.y 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.z 9702.a 1.a $1$ $77.471$ \(\Q\) None \(-1\) \(0\) \(3\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+q^{11}+\cdots\)
9702.2.a.ba 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(-4\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+q^{11}+\cdots\)
9702.2.a.bb 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(-4\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+q^{11}+\cdots\)
9702.2.a.bc 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(-3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-q^{11}+\cdots\)
9702.2.a.bd 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(-3\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+q^{11}+\cdots\)
9702.2.a.be 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+q^{11}+\cdots\)
9702.2.a.bf 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.bg 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-q^{11}+\cdots\)
9702.2.a.bh 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.bi 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.bj 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-q^{11}+\cdots\)
9702.2.a.bk 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-q^{11}-4q^{13}+q^{16}+\cdots\)
9702.2.a.bl 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-q^{11}-4q^{13}+q^{16}+\cdots\)
9702.2.a.bm 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-q^{11}-2q^{13}+q^{16}+\cdots\)
9702.2.a.bn 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-q^{11}+4q^{13}+q^{16}+\cdots\)
9702.2.a.bo 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-q^{11}+4q^{13}+q^{16}+\cdots\)
9702.2.a.bp 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+q^{11}-6q^{13}+q^{16}+\cdots\)
9702.2.a.bq 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+q^{11}-4q^{13}+q^{16}+\cdots\)
9702.2.a.br 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+q^{11}-q^{13}+q^{16}+\cdots\)
9702.2.a.bs 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+q^{11}+q^{13}+q^{16}+\cdots\)
9702.2.a.bt 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+q^{11}+2q^{13}+q^{16}+\cdots\)
9702.2.a.bu 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+q^{11}+4q^{13}+q^{16}+\cdots\)
9702.2.a.bv 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+q^{11}+4q^{13}+q^{16}+\cdots\)
9702.2.a.bw 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots\)
9702.2.a.bx 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.by 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.bz 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}-q^{11}+\cdots\)
9702.2.a.ca 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.cb 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.cc 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.cd 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-q^{11}+\cdots\)
9702.2.a.ce 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+q^{11}+\cdots\)
9702.2.a.cf 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+q^{11}+\cdots\)
9702.2.a.cg 9702.a 1.a $1$ $77.471$ \(\Q\) None \(1\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+q^{11}+\cdots\)
9702.2.a.ch 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-2+\beta )q^{5}-q^{8}+(2+\cdots)q^{10}+\cdots\)
9702.2.a.ci 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-4\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots\)
9702.2.a.cj 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
9702.2.a.ck 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta )q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
9702.2.a.cl 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-q^{11}+\cdots\)
9702.2.a.cm 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3\beta q^{5}-q^{8}-3\beta q^{10}+\cdots\)
9702.2.a.cn 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+q^{11}+\cdots\)
9702.2.a.co 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+q^{11}+3\beta q^{13}+\cdots\)
9702.2.a.cp 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3\beta q^{5}-q^{8}-3\beta q^{10}+\cdots\)
9702.2.a.cq 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+q^{11}-3\beta q^{13}+\cdots\)
9702.2.a.cr 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2\beta q^{5}-q^{8}-2\beta q^{10}+\cdots\)
9702.2.a.cs 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3\beta q^{5}-q^{8}-3\beta q^{10}+\cdots\)
9702.2.a.ct 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+q^{11}+\cdots\)
9702.2.a.cu 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.cv 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.cw 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.cx 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(2+\beta )q^{5}-q^{8}+(-2+\cdots)q^{10}+\cdots\)
9702.2.a.cy 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{11}+\cdots\)
9702.2.a.cz 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.da 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.db 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.dc 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.dd 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.de 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-q^{11}-\beta q^{13}+q^{16}+\cdots\)
9702.2.a.df 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2\beta q^{5}+q^{8}+2\beta q^{10}+\cdots\)
9702.2.a.dg 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.dh 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-q^{11}+3\beta q^{13}+\cdots\)
9702.2.a.di 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2\beta q^{5}+q^{8}+2\beta q^{10}+\cdots\)
9702.2.a.dj 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3\beta q^{5}+q^{8}+3\beta q^{10}+\cdots\)
9702.2.a.dk 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.dl 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-q^{11}-\beta q^{13}+q^{16}+\cdots\)
9702.2.a.dm 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-q^{11}+\cdots\)
9702.2.a.dn 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+q^{11}-\beta q^{13}+q^{16}+\cdots\)
9702.2.a.do 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3\beta q^{5}+q^{8}+3\beta q^{10}+\cdots\)
9702.2.a.dp 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+q^{11}+\cdots\)
9702.2.a.dq 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+q^{11}+\cdots\)
9702.2.a.dr 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{8}+(1+\beta )q^{10}+\cdots\)
9702.2.a.ds 9702.a 1.a $2$ $77.471$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{8}+(1+\beta )q^{10}+\cdots\)
9702.2.a.dt 9702.a 1.a $3$ $77.471$ 3.3.621.1 None \(-3\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta _{2}q^{5}-q^{8}+\beta _{2}q^{10}+\cdots\)
9702.2.a.du 9702.a 1.a $3$ $77.471$ 3.3.621.1 None \(-3\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{2}q^{5}-q^{8}-\beta _{2}q^{10}+\cdots\)
9702.2.a.dv 9702.a 1.a $3$ $77.471$ 3.3.2700.1 None \(-3\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta _{1}q^{5}-q^{8}+\beta _{1}q^{10}+\cdots\)
9702.2.a.dw 9702.a 1.a $3$ $77.471$ 3.3.2700.1 None \(-3\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots\)
9702.2.a.dx 9702.a 1.a $3$ $77.471$ 3.3.1304.1 None \(-3\) \(0\) \(2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta _{2})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.dy 9702.a 1.a $3$ $77.471$ 3.3.1304.1 None \(3\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.dz 9702.a 1.a $4$ $77.471$ 4.4.4352.1 None \(-4\) \(0\) \(-4\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta _{3})q^{5}-q^{8}+(1+\cdots)q^{10}+\cdots\)
9702.2.a.ea 9702.a 1.a $4$ $77.471$ 4.4.4352.1 None \(-4\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta _{3})q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots\)
9702.2.a.eb 9702.a 1.a $4$ $77.471$ 4.4.14336.1 None \(4\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{2}q^{5}+q^{8}+\beta _{2}q^{10}+\cdots\)
9702.2.a.ec 9702.a 1.a $4$ $77.471$ 4.4.14336.1 None \(4\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{2}q^{5}+q^{8}+\beta _{2}q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9702))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9702)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1386))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1617))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4851))\)\(^{\oplus 2}\)