Properties

Label 9196.2.a
Level $9196$
Weight $2$
Character orbit 9196.a
Rep. character $\chi_{9196}(1,\cdot)$
Character field $\Q$
Dimension $163$
Newform subspaces $24$
Sturm bound $2640$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 9196 = 2^{2} \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9196.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(2640\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9196))\).

Total New Old
Modular forms 1356 163 1193
Cusp forms 1285 163 1122
Eisenstein series 71 0 71

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

\(2\)\(11\)\(19\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(41\)
\(-\)\(+\)\(-\)\(+\)\(37\)
\(-\)\(-\)\(+\)\(+\)\(40\)
\(-\)\(-\)\(-\)\(-\)\(45\)
Plus space\(+\)\(77\)
Minus space\(-\)\(86\)

Trace form

\( 163 q - 2 q^{3} - 7 q^{5} + 3 q^{7} + 151 q^{9} + O(q^{10}) \) \( 163 q - 2 q^{3} - 7 q^{5} + 3 q^{7} + 151 q^{9} - 8 q^{13} + 2 q^{15} - q^{17} + q^{19} - 10 q^{21} - 8 q^{23} + 152 q^{25} - 20 q^{27} - 10 q^{29} + 4 q^{31} - 19 q^{35} - 22 q^{37} - 4 q^{39} - 18 q^{41} - 13 q^{43} - 39 q^{45} - 7 q^{47} + 138 q^{49} - 34 q^{51} - 12 q^{53} + 2 q^{57} + 2 q^{59} - 19 q^{61} + 19 q^{63} + 8 q^{65} - 4 q^{67} + 4 q^{69} + 18 q^{71} + 3 q^{73} + 28 q^{75} + 24 q^{79} + 135 q^{81} + 28 q^{83} - 19 q^{85} + 32 q^{87} - 24 q^{89} - 20 q^{91} + 36 q^{93} - q^{95} - 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9196))\) 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 11 19
9196.2.a.a 9196.a 1.a $1$ $73.430$ \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}-2q^{9}-6q^{13}+\cdots\)
9196.2.a.b 9196.a 1.a $1$ $73.430$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}+2q^{13}-q^{15}+\cdots\)
9196.2.a.c 9196.a 1.a $1$ $73.430$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}-2q^{9}+6q^{13}+\cdots\)
9196.2.a.d 9196.a 1.a $1$ $73.430$ \(\Q\) None \(0\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-3q^{9}-q^{13}+7q^{17}-q^{19}+\cdots\)
9196.2.a.e 9196.a 1.a $1$ $73.430$ \(\Q\) None \(0\) \(0\) \(-3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-3q^{9}+q^{13}-7q^{17}+q^{19}+\cdots\)
9196.2.a.f 9196.a 1.a $1$ $73.430$ \(\Q\) None \(0\) \(2\) \(-1\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+3q^{7}+q^{9}+4q^{13}+\cdots\)
9196.2.a.g 9196.a 1.a $1$ $73.430$ \(\Q\) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}+q^{9}-4q^{13}+4q^{15}+\cdots\)
9196.2.a.h 9196.a 1.a $2$ $73.430$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}+\beta q^{7}-2\beta q^{9}+\cdots\)
9196.2.a.i 9196.a 1.a $6$ $73.430$ 6.6.34963625.1 None \(0\) \(-2\) \(-7\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
9196.2.a.j 9196.a 1.a $6$ $73.430$ 6.6.34963625.1 None \(0\) \(-2\) \(-7\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
9196.2.a.k 9196.a 1.a $6$ $73.430$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-2\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{4}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9196.2.a.l 9196.a 1.a $6$ $73.430$ 6.6.114134848.1 None \(0\) \(0\) \(-4\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+(-\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
9196.2.a.m 9196.a 1.a $6$ $73.430$ 6.6.114134848.1 None \(0\) \(0\) \(-4\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+(\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
9196.2.a.n 9196.a 1.a $6$ $73.430$ 6.6.744786576.1 None \(0\) \(1\) \(5\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{5})q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
9196.2.a.o 9196.a 1.a $7$ $73.430$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-1\) \(3\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
9196.2.a.p 9196.a 1.a $7$ $73.430$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-1\) \(3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{2}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
9196.2.a.q 9196.a 1.a $8$ $73.430$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+(-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots\)
9196.2.a.r 9196.a 1.a $8$ $73.430$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-1\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+(\beta _{2}-\beta _{3}-\beta _{6})q^{7}+\cdots\)
9196.2.a.s 9196.a 1.a $10$ $73.430$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(8\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{7})q^{5}+(-\beta _{5}-\beta _{8}+\cdots)q^{7}+\cdots\)
9196.2.a.t 9196.a 1.a $10$ $73.430$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(8\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{7})q^{5}+(\beta _{5}+\beta _{8})q^{7}+\cdots\)
9196.2.a.u 9196.a 1.a $14$ $73.430$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-2\) \(-6\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{9}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
9196.2.a.v 9196.a 1.a $14$ $73.430$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-2\) \(-6\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{9}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
9196.2.a.w 9196.a 1.a $20$ $73.430$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(6\) \(2\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{14}q^{5}+\beta _{10}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
9196.2.a.x 9196.a 1.a $20$ $73.430$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(6\) \(2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{14}q^{5}-\beta _{10}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9196))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9196)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(418))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(836))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2299))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4598))\)\(^{\oplus 2}\)