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Properties

Label 9350.2.a
Level $9350$
Weight $2$
Character orbit 9350.a
Rep. character $\chi_{9350}(1,\cdot)$
Character field $\Q$
Dimension $256$
Newform subspaces $85$
Sturm bound $3240$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 9350 = 2 \cdot 5^{2} \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9350.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 85 \)
Sturm bound: \(3240\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9350))\).

Total New Old
Modular forms 1644 256 1388
Cusp forms 1597 256 1341
Eisenstein series 47 0 47

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

\(2\)\(5\)\(11\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)\(15\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(16\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(13\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(19\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(15\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(21\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(16\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(12\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(19\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(21\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(21\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(11\)
Plus space\(+\)\(107\)
Minus space\(-\)\(149\)

Trace form

\( 256 q + 256 q^{4} - 8 q^{6} + 16 q^{7} + 252 q^{9} + O(q^{10}) \) \( 256 q + 256 q^{4} - 8 q^{6} + 16 q^{7} + 252 q^{9} - 2 q^{11} + 16 q^{13} - 16 q^{14} + 256 q^{16} - 16 q^{18} + 48 q^{19} + 24 q^{21} + 2 q^{22} - 32 q^{23} - 8 q^{24} + 4 q^{26} + 16 q^{28} - 24 q^{29} + 40 q^{31} - 4 q^{33} - 4 q^{34} + 252 q^{36} + 24 q^{37} + 4 q^{38} + 40 q^{39} + 8 q^{41} + 16 q^{43} - 2 q^{44} - 16 q^{46} + 12 q^{47} + 300 q^{49} + 16 q^{52} - 32 q^{54} - 16 q^{56} + 8 q^{57} + 8 q^{58} - 16 q^{59} + 40 q^{61} + 16 q^{62} + 40 q^{63} + 256 q^{64} + 72 q^{67} + 56 q^{69} + 56 q^{71} - 16 q^{72} + 64 q^{73} + 8 q^{74} + 48 q^{76} + 4 q^{77} - 8 q^{78} + 64 q^{79} + 304 q^{81} + 24 q^{82} + 40 q^{83} + 24 q^{84} + 20 q^{86} + 48 q^{87} + 2 q^{88} + 44 q^{89} + 128 q^{91} - 32 q^{92} + 32 q^{93} - 8 q^{96} + 16 q^{97} + 24 q^{98} + 54 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9350))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 11 17
9350.2.a.a 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.a \(-1\) \(-2\) \(0\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
9350.2.a.b 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.b.a \(-1\) \(-2\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots\)
9350.2.a.c 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.b.b \(-1\) \(-2\) \(0\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots\)
9350.2.a.d 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.d \(-1\) \(-2\) \(0\) \(5\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}+5q^{7}-q^{8}+\cdots\)
9350.2.a.e 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.a.i \(-1\) \(-1\) \(0\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
9350.2.a.f 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.f \(-1\) \(-1\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
9350.2.a.g 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.g \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
9350.2.a.h 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.h \(-1\) \(1\) \(0\) \(-3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
9350.2.a.i 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.i \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
9350.2.a.j 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.j \(-1\) \(1\) \(0\) \(-1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
9350.2.a.k 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.a.h \(-1\) \(1\) \(0\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
9350.2.a.l 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.l \(-1\) \(1\) \(0\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots\)
9350.2.a.m 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.m \(-1\) \(2\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-2q^{7}-q^{8}+\cdots\)
9350.2.a.n 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.n \(-1\) \(2\) \(0\) \(-2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-2q^{7}-q^{8}+\cdots\)
9350.2.a.o 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.o \(-1\) \(2\) \(0\) \(2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}+2q^{7}-q^{8}+\cdots\)
9350.2.a.p 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.a.g \(-1\) \(3\) \(0\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+4q^{7}-q^{8}+\cdots\)
9350.2.a.q 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.q \(-1\) \(3\) \(0\) \(5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+5q^{7}-q^{8}+\cdots\)
9350.2.a.r 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.q \(1\) \(-3\) \(0\) \(-5\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-3q^{6}-5q^{7}+q^{8}+\cdots\)
9350.2.a.s 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.o \(1\) \(-2\) \(0\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-2q^{7}+q^{8}+\cdots\)
9350.2.a.t 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.m \(1\) \(-2\) \(0\) \(2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+2q^{7}+q^{8}+\cdots\)
9350.2.a.u 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.n \(1\) \(-2\) \(0\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+2q^{7}+q^{8}+\cdots\)
9350.2.a.v 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.l \(1\) \(-1\) \(0\) \(-3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-3q^{7}+q^{8}+\cdots\)
9350.2.a.w 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.a.f \(1\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots\)
9350.2.a.x 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.i \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
9350.2.a.y 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.j \(1\) \(-1\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
9350.2.a.z 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.h \(1\) \(-1\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\)
9350.2.a.ba 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.a.e \(1\) \(-1\) \(0\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots\)
9350.2.a.bb 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.a.c \(1\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-3q^{9}-q^{11}+6q^{13}+\cdots\)
9350.2.a.bc 9350.a 1.a $1$ $74.660$ \(\Q\) None 374.2.a.a \(1\) \(0\) \(0\) \(2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
9350.2.a.bd 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.a.d \(1\) \(0\) \(0\) \(4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{7}+q^{8}-3q^{9}+q^{11}+\cdots\)
9350.2.a.be 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.g \(1\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
9350.2.a.bf 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.f \(1\) \(1\) \(0\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
9350.2.a.bg 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.a.b \(1\) \(1\) \(0\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
9350.2.a.bh 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.d \(1\) \(2\) \(0\) \(-5\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}-5q^{7}+q^{8}+\cdots\)
9350.2.a.bi 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.b.a \(1\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots\)
9350.2.a.bj 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.b.b \(1\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots\)
9350.2.a.bk 9350.a 1.a $1$ $74.660$ \(\Q\) None 9350.2.a.a \(1\) \(2\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
9350.2.a.bl 9350.a 1.a $1$ $74.660$ \(\Q\) None 1870.2.a.a \(1\) \(3\) \(0\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots\)
9350.2.a.bm 9350.a 1.a $2$ $74.660$ \(\Q(\sqrt{73}) \) None 9350.2.a.bm \(-2\) \(-2\) \(0\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
9350.2.a.bn 9350.a 1.a $2$ $74.660$ \(\Q(\sqrt{17}) \) None 1870.2.a.m \(-2\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+(1+\cdots)q^{9}+\cdots\)
9350.2.a.bo 9350.a 1.a $2$ $74.660$ \(\Q(\sqrt{7}) \) None 9350.2.a.bo \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-\beta q^{7}-q^{8}+\cdots\)
9350.2.a.bp 9350.a 1.a $2$ $74.660$ \(\Q(\sqrt{2}) \) None 9350.2.a.bp \(-2\) \(2\) \(0\) \(-6\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
9350.2.a.bq 9350.a 1.a $2$ $74.660$ \(\Q(\sqrt{2}) \) None 1870.2.a.l \(-2\) \(2\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
9350.2.a.br 9350.a 1.a $2$ $74.660$ \(\Q(\sqrt{2}) \) None 9350.2.a.bp \(2\) \(-2\) \(0\) \(6\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
9350.2.a.bs 9350.a 1.a $2$ $74.660$ \(\Q(\sqrt{3}) \) None 1870.2.a.k \(2\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+(-1+\beta )q^{7}+\cdots\)
9350.2.a.bt 9350.a 1.a $2$ $74.660$ \(\Q(\sqrt{7}) \) None 9350.2.a.bo \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-\beta q^{7}+q^{8}+\cdots\)
9350.2.a.bu 9350.a 1.a $2$ $74.660$ \(\Q(\sqrt{73}) \) None 9350.2.a.bm \(2\) \(2\) \(0\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
9350.2.a.bv 9350.a 1.a $2$ $74.660$ \(\Q(\sqrt{2}) \) None 1870.2.a.j \(2\) \(2\) \(0\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
9350.2.a.bw 9350.a 1.a $3$ $74.660$ 3.3.257.1 None 374.2.a.c \(-3\) \(-3\) \(0\) \(-7\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)
9350.2.a.bx 9350.a 1.a $3$ $74.660$ 3.3.148.1 None 9350.2.a.bx \(-3\) \(-3\) \(0\) \(3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)
9350.2.a.by 9350.a 1.a $3$ $74.660$ 3.3.940.1 None 1870.2.a.r \(-3\) \(0\) \(0\) \(2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(1+\beta _{2})q^{7}+\cdots\)
9350.2.a.bz 9350.a 1.a $3$ $74.660$ 3.3.148.1 None 9350.2.a.bz \(-3\) \(3\) \(0\) \(5\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{2})q^{6}+\cdots\)
9350.2.a.ca 9350.a 1.a $3$ $74.660$ 3.3.148.1 None 1870.2.a.q \(-3\) \(3\) \(0\) \(6\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{2})q^{6}+\cdots\)
9350.2.a.cb 9350.a 1.a $3$ $74.660$ 3.3.756.1 None 1870.2.a.p \(3\) \(-3\) \(0\) \(-6\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
9350.2.a.cc 9350.a 1.a $3$ $74.660$ 3.3.148.1 None 9350.2.a.bz \(3\) \(-3\) \(0\) \(-5\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(-1+\beta _{2})q^{6}+\cdots\)
9350.2.a.cd 9350.a 1.a $3$ $74.660$ 3.3.564.1 None 1870.2.a.n \(3\) \(-1\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
9350.2.a.ce 9350.a 1.a $3$ $74.660$ 3.3.148.1 None 1870.2.a.o \(3\) \(-1\) \(0\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
9350.2.a.cf 9350.a 1.a $3$ $74.660$ 3.3.785.1 None 374.2.a.b \(3\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
9350.2.a.cg 9350.a 1.a $3$ $74.660$ 3.3.148.1 None 9350.2.a.bx \(3\) \(3\) \(0\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)
9350.2.a.ch 9350.a 1.a $4$ $74.660$ 4.4.17428.1 None 1870.2.a.t \(-4\) \(-3\) \(0\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
9350.2.a.ci 9350.a 1.a $4$ $74.660$ 4.4.25492.1 None 1870.2.a.u \(-4\) \(-3\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
9350.2.a.cj 9350.a 1.a $4$ $74.660$ 4.4.17417.1 None 374.2.a.e \(-4\) \(-1\) \(0\) \(-1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{3}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
9350.2.a.ck 9350.a 1.a $4$ $74.660$ 4.4.23252.1 None 1870.2.a.s \(-4\) \(3\) \(0\) \(4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
9350.2.a.cl 9350.a 1.a $4$ $74.660$ 4.4.55585.1 None 374.2.a.d \(4\) \(-1\) \(0\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{2}+\beta _{3})q^{7}+\cdots\)
9350.2.a.cm 9350.a 1.a $5$ $74.660$ 5.5.3484752.1 None 9350.2.a.cm \(-5\) \(-4\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
9350.2.a.cn 9350.a 1.a $5$ $74.660$ 5.5.815952.1 None 9350.2.a.cn \(-5\) \(1\) \(0\) \(-7\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+(-1+\cdots)q^{7}+\cdots\)
9350.2.a.co 9350.a 1.a $5$ $74.660$ 5.5.126032.1 None 1870.2.b.c \(-5\) \(1\) \(0\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{4}q^{3}+q^{4}-\beta _{4}q^{6}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
9350.2.a.cp 9350.a 1.a $5$ $74.660$ 5.5.2054224.1 None 9350.2.a.cp \(-5\) \(3\) \(0\) \(5\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
9350.2.a.cq 9350.a 1.a $5$ $74.660$ 5.5.2118096.1 None 9350.2.a.cq \(-5\) \(3\) \(0\) \(7\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
9350.2.a.cr 9350.a 1.a $5$ $74.660$ 5.5.2118096.1 None 9350.2.a.cq \(5\) \(-3\) \(0\) \(-7\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
9350.2.a.cs 9350.a 1.a $5$ $74.660$ 5.5.2054224.1 None 9350.2.a.cp \(5\) \(-3\) \(0\) \(-5\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
9350.2.a.ct 9350.a 1.a $5$ $74.660$ 5.5.126032.1 None 1870.2.b.c \(5\) \(-1\) \(0\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{4}q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
9350.2.a.cu 9350.a 1.a $5$ $74.660$ 5.5.815952.1 None 9350.2.a.cn \(5\) \(-1\) \(0\) \(7\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+(1+\beta _{4})q^{7}+\cdots\)
9350.2.a.cv 9350.a 1.a $5$ $74.660$ 5.5.3102944.1 None 1870.2.a.v \(5\) \(1\) \(0\) \(8\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{3}q^{3}+q^{4}-\beta _{3}q^{6}+(2-\beta _{2}+\cdots)q^{7}+\cdots\)
9350.2.a.cw 9350.a 1.a $5$ $74.660$ 5.5.3484752.1 None 9350.2.a.cm \(5\) \(4\) \(0\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
9350.2.a.cx 9350.a 1.a $6$ $74.660$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 9350.2.a.cx \(-6\) \(-1\) \(0\) \(-8\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
9350.2.a.cy 9350.a 1.a $6$ $74.660$ 6.6.92511952.1 None 9350.2.a.cy \(-6\) \(-1\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{2}-\beta _{4})q^{3}+q^{4}+(-\beta _{2}+\beta _{4}+\cdots)q^{6}+\cdots\)
9350.2.a.cz 9350.a 1.a $6$ $74.660$ 6.6.92511952.1 None 9350.2.a.cy \(6\) \(1\) \(0\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-\beta _{2}+\beta _{4})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
9350.2.a.da 9350.a 1.a $6$ $74.660$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 9350.2.a.cx \(6\) \(1\) \(0\) \(8\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(1-\beta _{5})q^{7}+\cdots\)
9350.2.a.db 9350.a 1.a $7$ $74.660$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 1870.2.b.d \(-7\) \(3\) \(0\) \(4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
9350.2.a.dc 9350.a 1.a $7$ $74.660$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 1870.2.b.d \(7\) \(-3\) \(0\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
9350.2.a.dd 9350.a 1.a $13$ $74.660$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 1870.2.b.e \(-13\) \(-3\) \(0\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{11}q^{7}+\cdots\)
9350.2.a.de 9350.a 1.a $13$ $74.660$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 1870.2.b.f \(-13\) \(-1\) \(0\) \(-2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{4}q^{7}+\cdots\)
9350.2.a.df 9350.a 1.a $13$ $74.660$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 1870.2.b.f \(13\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{4}q^{7}+\cdots\)
9350.2.a.dg 9350.a 1.a $13$ $74.660$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 1870.2.b.e \(13\) \(3\) \(0\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{11}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9350))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9350)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(374))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(935))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1870))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4675))\)\(^{\oplus 2}\)