Properties

Label 9036.2.a
Level $9036$
Weight $2$
Character orbit 9036.a
Rep. character $\chi_{9036}(1,\cdot)$
Character field $\Q$
Dimension $103$
Newform subspaces $15$
Sturm bound $3024$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 9036 = 2^{2} \cdot 3^{2} \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9036.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(3024\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9036))\).

Total New Old
Modular forms 1524 103 1421
Cusp forms 1501 103 1398
Eisenstein series 23 0 23

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

\(2\)\(3\)\(251\)FrickeDim
\(-\)\(+\)\(+\)$-$\(20\)
\(-\)\(+\)\(-\)$+$\(20\)
\(-\)\(-\)\(+\)$+$\(28\)
\(-\)\(-\)\(-\)$-$\(35\)
Plus space\(+\)\(48\)
Minus space\(-\)\(55\)

Trace form

\( 103 q + 2 q^{7} + O(q^{10}) \) \( 103 q + 2 q^{7} - 4 q^{11} - 6 q^{13} - 4 q^{19} - 4 q^{23} + 103 q^{25} - 12 q^{31} + 2 q^{35} + 2 q^{37} - 4 q^{41} - 12 q^{43} + 73 q^{49} - 6 q^{53} - 6 q^{55} - 10 q^{59} - 38 q^{61} - 15 q^{65} + 10 q^{67} + 4 q^{71} + 18 q^{73} - 24 q^{77} + 10 q^{79} + 23 q^{83} + 2 q^{85} - 12 q^{89} + 4 q^{91} - 12 q^{95} - 40 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9036))\) 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 3 251
9036.2.a.a 9036.a 1.a $1$ $72.153$ \(\Q\) None \(0\) \(0\) \(-3\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-3q^{7}-6q^{13}+7q^{17}-6q^{19}+\cdots\)
9036.2.a.b 9036.a 1.a $1$ $72.153$ \(\Q\) None \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}+2q^{11}-q^{13}-5q^{19}+\cdots\)
9036.2.a.c 9036.a 1.a $1$ $72.153$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-q^{13}-6q^{17}+5q^{19}+9q^{23}+\cdots\)
9036.2.a.d 9036.a 1.a $1$ $72.153$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{7}-q^{13}+6q^{17}+5q^{19}-9q^{23}+\cdots\)
9036.2.a.e 9036.a 1.a $1$ $72.153$ \(\Q\) None \(0\) \(0\) \(1\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+5q^{7}+6q^{11}-2q^{13}+3q^{17}+\cdots\)
9036.2.a.f 9036.a 1.a $1$ $72.153$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}-6q^{11}+7q^{13}-8q^{17}+\cdots\)
9036.2.a.g 9036.a 1.a $1$ $72.153$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}+2q^{11}+2q^{13}+5q^{17}+\cdots\)
9036.2.a.h 9036.a 1.a $6$ $72.153$ 6.6.4443861.1 None \(0\) \(0\) \(4\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
9036.2.a.i 9036.a 1.a $7$ $72.153$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(2\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{5}+(-1-\beta _{6})q^{7}+(1-\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots\)
9036.2.a.j 9036.a 1.a $9$ $72.153$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{5}-\beta _{7}q^{7}+(-1-\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)
9036.2.a.k 9036.a 1.a $10$ $72.153$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-5\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+\beta _{2}q^{11}+\cdots\)
9036.2.a.l 9036.a 1.a $12$ $72.153$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-7\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}+\beta _{6}q^{7}+(1+\beta _{4}-\beta _{6}+\cdots)q^{11}+\cdots\)
9036.2.a.m 9036.a 1.a $14$ $72.153$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(2\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{5}+(1-\beta _{9})q^{7}+(-1+\beta _{8})q^{11}+\cdots\)
9036.2.a.n 9036.a 1.a $19$ $72.153$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}+\beta _{10}q^{7}+(-1+\beta _{4})q^{11}+\cdots\)
9036.2.a.o 9036.a 1.a $19$ $72.153$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+\beta _{10}q^{7}+(1-\beta _{4})q^{11}+\beta _{8}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9036))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9036)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(502))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(753))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1004))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1506))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2259))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3012))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4518))\)\(^{\oplus 2}\)