Properties

Label 8624.2.a
Level $8624$
Weight $2$
Character orbit 8624.a
Rep. character $\chi_{8624}(1,\cdot)$
Character field $\Q$
Dimension $205$
Newform subspaces $85$
Sturm bound $2688$
Trace bound $37$

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Defining parameters

Level: \( N \) \(=\) \( 8624 = 2^{4} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8624.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 85 \)
Sturm bound: \(2688\)
Trace bound: \(37\)
Distinguishing \(T_p\): \(3\), \(5\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8624))\).

Total New Old
Modular forms 1392 205 1187
Cusp forms 1297 205 1092
Eisenstein series 95 0 95

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

\(2\)\(7\)\(11\)FrickeDim
\(+\)\(+\)\(+\)$+$\(20\)
\(+\)\(+\)\(-\)$-$\(32\)
\(+\)\(-\)\(+\)$-$\(30\)
\(+\)\(-\)\(-\)$+$\(21\)
\(-\)\(+\)\(+\)$-$\(24\)
\(-\)\(+\)\(-\)$+$\(24\)
\(-\)\(-\)\(+\)$+$\(27\)
\(-\)\(-\)\(-\)$-$\(27\)
Plus space\(+\)\(92\)
Minus space\(-\)\(113\)

Trace form

\( 205 q - 2 q^{3} - 2 q^{5} + 205 q^{9} + O(q^{10}) \) \( 205 q - 2 q^{3} - 2 q^{5} + 205 q^{9} + 3 q^{11} - 2 q^{13} + 2 q^{15} + 2 q^{17} - 12 q^{19} - 6 q^{23} + 207 q^{25} - 14 q^{27} + 6 q^{29} - 18 q^{31} - 10 q^{37} - 16 q^{39} + 2 q^{41} - 16 q^{43} - 2 q^{45} + 28 q^{47} + 12 q^{51} - 2 q^{53} + 4 q^{55} + 8 q^{57} - 22 q^{59} + 6 q^{61} + 28 q^{65} + 14 q^{67} + 24 q^{69} + 6 q^{71} + 2 q^{73} - 72 q^{75} - 36 q^{79} + 213 q^{81} + 32 q^{83} + 4 q^{85} - 40 q^{87} - 2 q^{89} + 24 q^{93} - 48 q^{95} - 10 q^{97} + 9 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8624))\) 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 7 11
8624.2.a.a 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-3\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}+6q^{9}+q^{11}+4q^{13}+\cdots\)
8624.2.a.b 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-3\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+2q^{5}+6q^{9}+q^{11}-7q^{13}+\cdots\)
8624.2.a.c 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-3\) \(3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+3q^{5}+6q^{9}+q^{11}-9q^{15}+\cdots\)
8624.2.a.d 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-3\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+4q^{5}+6q^{9}+q^{11}+q^{13}+\cdots\)
8624.2.a.e 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-2\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}+q^{9}+q^{11}-4q^{13}+\cdots\)
8624.2.a.f 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}+q^{11}-2q^{13}+2q^{17}+\cdots\)
8624.2.a.g 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-2\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+q^{9}-q^{11}-2q^{13}+\cdots\)
8624.2.a.h 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-2\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{5}+q^{9}-q^{11}+2q^{13}+\cdots\)
8624.2.a.i 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-2q^{9}+q^{11}-3q^{13}+\cdots\)
8624.2.a.j 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{9}-q^{11}-4q^{13}+\cdots\)
8624.2.a.k 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{9}+q^{11}-q^{13}-6q^{17}+\cdots\)
8624.2.a.l 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{9}+q^{11}+5q^{13}+6q^{17}+\cdots\)
8624.2.a.m 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}-q^{11}-q^{15}+2q^{17}+\cdots\)
8624.2.a.n 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}-q^{11}+4q^{13}+\cdots\)
8624.2.a.o 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-3q^{9}+q^{11}-2q^{13}-2q^{17}+\cdots\)
8624.2.a.p 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{9}+q^{11}+6q^{13}-2q^{19}-4q^{23}+\cdots\)
8624.2.a.q 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-3q^{9}+q^{11}-2q^{13}+2q^{17}+\cdots\)
8624.2.a.r 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-3q^{9}+q^{11}-2q^{13}+4q^{17}+\cdots\)
8624.2.a.s 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(1\) \(-3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-2q^{9}+q^{11}+4q^{13}+\cdots\)
8624.2.a.t 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{9}+q^{11}-5q^{13}-6q^{17}+\cdots\)
8624.2.a.u 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{9}+q^{11}+q^{13}+6q^{17}+\cdots\)
8624.2.a.v 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-2q^{9}+q^{11}+3q^{13}+\cdots\)
8624.2.a.w 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(1\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-2q^{9}+q^{11}+4q^{13}+\cdots\)
8624.2.a.x 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(2\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{5}+q^{9}-q^{11}-2q^{13}+\cdots\)
8624.2.a.y 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+q^{9}-q^{11}+2q^{13}+\cdots\)
8624.2.a.z 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
8624.2.a.ba 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(2\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+q^{9}+q^{11}-4q^{15}+\cdots\)
8624.2.a.bb 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(2\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}+q^{11}+2q^{13}-2q^{17}+\cdots\)
8624.2.a.bc 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
8624.2.a.bd 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(3\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-4q^{5}+6q^{9}+q^{11}-q^{13}+\cdots\)
8624.2.a.be 8624.a 1.a $1$ $68.863$ \(\Q\) None \(0\) \(3\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{5}+6q^{9}+q^{11}+7q^{13}+\cdots\)
8624.2.a.bf 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-1-\beta )q^{5}+(3+2\beta )q^{9}+\cdots\)
8624.2.a.bg 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+\beta q^{5}-2\beta q^{9}-q^{11}+\cdots\)
8624.2.a.bh 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(2+\beta )q^{5}-2\beta q^{9}+\cdots\)
8624.2.a.bi 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}-q^{11}+\cdots\)
8624.2.a.bj 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{5}+3q^{9}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
8624.2.a.bk 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{5}+4q^{9}-q^{11}+\cdots\)
8624.2.a.bl 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2\beta q^{5}-3q^{9}-q^{11}+3\beta q^{13}-2\beta q^{17}+\cdots\)
8624.2.a.bm 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-3q^{9}-q^{11}-3\beta q^{13}-\beta q^{17}+\cdots\)
8624.2.a.bn 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2\beta q^{5}-3q^{9}-q^{11}-\beta q^{13}+2\beta q^{17}+\cdots\)
8624.2.a.bo 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-3q^{9}-q^{11}-2\beta q^{13}-\beta q^{17}+\cdots\)
8624.2.a.bp 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-3q^{9}+q^{11}+\beta q^{17}-\beta q^{19}+\cdots\)
8624.2.a.bq 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-\beta q^{5}-q^{9}-q^{11}-2q^{15}+\cdots\)
8624.2.a.br 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{5}-q^{9}-q^{11}-2\beta q^{13}+\cdots\)
8624.2.a.bs 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-3\beta q^{5}-q^{9}+q^{11}-6q^{15}+\cdots\)
8624.2.a.bt 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-\beta q^{5}-q^{9}+q^{11}-2q^{15}+\cdots\)
8624.2.a.bu 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{9}+q^{11}+\beta q^{13}+5\beta q^{17}+\cdots\)
8624.2.a.bv 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{5}-q^{9}+q^{11}+2q^{15}+\cdots\)
8624.2.a.bw 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{5}-q^{9}+q^{11}+2\beta q^{13}+\cdots\)
8624.2.a.bx 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}-\beta q^{5}+5q^{9}+q^{11}+\beta q^{13}+\cdots\)
8624.2.a.by 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+5q^{9}+q^{11}+\beta q^{13}-\beta q^{17}+\cdots\)
8624.2.a.bz 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}+5q^{9}+q^{11}-3\beta q^{13}+2\beta q^{17}+\cdots\)
8624.2.a.ca 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1+\beta )q^{5}+4q^{9}-q^{11}+5q^{13}+\cdots\)
8624.2.a.cb 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}+q^{11}+\cdots\)
8624.2.a.cc 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-2+\beta )q^{5}+2\beta q^{9}+\cdots\)
8624.2.a.cd 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+\beta q^{5}+2\beta q^{9}-q^{11}+\cdots\)
8624.2.a.ce 8624.a 1.a $2$ $68.863$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+2q^{5}+(3+2\beta )q^{9}+q^{11}+\cdots\)
8624.2.a.cf 8624.a 1.a $3$ $68.863$ \(\Q(\zeta_{14})^+\) None \(0\) \(-5\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{3}+(-1+3\beta _{1}-2\beta _{2})q^{5}+\cdots\)
8624.2.a.cg 8624.a 1.a $3$ $68.863$ 3.3.257.1 None \(0\) \(-3\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
8624.2.a.ch 8624.a 1.a $3$ $68.863$ \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(2+\beta _{1}-\beta _{2})q^{5}+\cdots\)
8624.2.a.ci 8624.a 1.a $3$ $68.863$ 3.3.321.1 None \(0\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
8624.2.a.cj 8624.a 1.a $3$ $68.863$ 3.3.1016.1 None \(0\) \(-1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
8624.2.a.ck 8624.a 1.a $3$ $68.863$ 3.3.257.1 None \(0\) \(-1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{9}+\cdots\)
8624.2.a.cl 8624.a 1.a $3$ $68.863$ 3.3.257.1 None \(0\) \(1\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{9}+\cdots\)
8624.2.a.cm 8624.a 1.a $3$ $68.863$ 3.3.229.1 None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+\beta _{2}q^{5}+(1-\beta _{1})q^{9}-q^{11}+\cdots\)
8624.2.a.cn 8624.a 1.a $3$ $68.863$ 3.3.321.1 None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(1-\beta _{1}-2\beta _{2})q^{9}+\cdots\)
8624.2.a.co 8624.a 1.a $3$ $68.863$ \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(-6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+(-2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
8624.2.a.cp 8624.a 1.a $3$ $68.863$ 3.3.257.1 None \(0\) \(3\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
8624.2.a.cq 8624.a 1.a $3$ $68.863$ \(\Q(\zeta_{14})^+\) None \(0\) \(5\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{3}+(-2+\beta _{1}-3\beta _{2})q^{5}+\cdots\)
8624.2.a.cr 8624.a 1.a $4$ $68.863$ 4.4.89289.1 None \(0\) \(-2\) \(4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{5}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
8624.2.a.cs 8624.a 1.a $4$ $68.863$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-2\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
8624.2.a.ct 8624.a 1.a $4$ $68.863$ 4.4.9248.1 None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{9}-q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots\)
8624.2.a.cu 8624.a 1.a $4$ $68.863$ 4.4.9248.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{3}q^{9}+q^{11}+\cdots\)
8624.2.a.cv 8624.a 1.a $4$ $68.863$ \(\Q(\sqrt{7}, \sqrt{15})\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+\beta _{2}q^{5}+(2-\beta _{3})q^{9}-q^{11}+\cdots\)
8624.2.a.cw 8624.a 1.a $4$ $68.863$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+3q^{9}-q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots\)
8624.2.a.cx 8624.a 1.a $4$ $68.863$ 4.4.301088.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(4+\beta _{3})q^{9}-q^{11}+\cdots\)
8624.2.a.cy 8624.a 1.a $4$ $68.863$ 4.4.11348.1 None \(0\) \(1\) \(-5\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(2+\beta _{2}-\beta _{3})q^{9}+\cdots\)
8624.2.a.cz 8624.a 1.a $4$ $68.863$ 4.4.89289.1 None \(0\) \(2\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
8624.2.a.da 8624.a 1.a $5$ $68.863$ 5.5.352076.1 None \(0\) \(-3\) \(4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(1-\beta _{1}+\beta _{4})q^{5}+\cdots\)
8624.2.a.db 8624.a 1.a $5$ $68.863$ 5.5.559701.1 None \(0\) \(-1\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{9}+\cdots\)
8624.2.a.dc 8624.a 1.a $5$ $68.863$ 5.5.559701.1 None \(0\) \(1\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{9}+\cdots\)
8624.2.a.dd 8624.a 1.a $5$ $68.863$ 5.5.352076.1 None \(0\) \(3\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{4})q^{5}+\cdots\)
8624.2.a.de 8624.a 1.a $8$ $68.863$ 8.8.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{5}+(1+\cdots)q^{9}+\cdots\)
8624.2.a.df 8624.a 1.a $10$ $68.863$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{6}q^{5}+(2+\beta _{2})q^{9}-q^{11}+\cdots\)
8624.2.a.dg 8624.a 1.a $12$ $68.863$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{9}q^{5}+(3+\beta _{2})q^{9}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8624))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8624)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4312))\)\(^{\oplus 2}\)