Properties

Label 2496.2.c
Level $2496$
Weight $2$
Character orbit 2496.c
Rep. character $\chi_{2496}(961,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $18$
Sturm bound $896$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2496.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(896\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(23\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2496, [\chi])\).

Total New Old
Modular forms 472 56 416
Cusp forms 424 56 368
Eisenstein series 48 0 48

Trace form

\( 56 q + 56 q^{9} + O(q^{10}) \) \( 56 q + 56 q^{9} - 8 q^{13} + 16 q^{17} - 72 q^{25} - 56 q^{49} - 16 q^{61} - 16 q^{65} + 56 q^{81} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2496, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2496.2.c.a 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2iq^{5}+iq^{7}+q^{9}+iq^{11}+\cdots\)
2496.2.c.b 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}-2iq^{7}+q^{9}-3iq^{11}+\cdots\)
2496.2.c.c 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-iq^{7}+q^{9}+iq^{11}+(-3-i)q^{13}+\cdots\)
2496.2.c.d 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\zeta_{6}q^{7}+q^{9}-\zeta_{6}q^{11}+(1-\zeta_{6})q^{13}+\cdots\)
2496.2.c.e 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\zeta_{6}q^{5}+q^{9}+\zeta_{6}q^{11}+(1-\zeta_{6})q^{13}+\cdots\)
2496.2.c.f 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}+iq^{7}+q^{9}+(3-i)q^{13}+\cdots\)
2496.2.c.g 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}-iq^{7}+q^{9}+2iq^{11}+\cdots\)
2496.2.c.h 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+2iq^{5}-iq^{7}+q^{9}-iq^{11}+\cdots\)
2496.2.c.i 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{5}+2iq^{7}+q^{9}+3iq^{11}+\cdots\)
2496.2.c.j 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{7}+q^{9}-iq^{11}+(-3-i)q^{13}+\cdots\)
2496.2.c.k 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\zeta_{6}q^{7}+q^{9}-\zeta_{6}q^{11}+(1+\zeta_{6})q^{13}+\cdots\)
2496.2.c.l 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\zeta_{6}q^{5}+q^{9}-\zeta_{6}q^{11}+(1-\zeta_{6})q^{13}+\cdots\)
2496.2.c.m 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{5}-iq^{7}+q^{9}+(3-i)q^{13}+\cdots\)
2496.2.c.n 2496.c 13.b $2$ $19.931$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{5}+iq^{7}+q^{9}-2iq^{11}+\cdots\)
2496.2.c.o 2496.c 13.b $6$ $19.931$ 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
2496.2.c.p 2496.c 13.b $6$ $19.931$ 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
2496.2.c.q 2496.c 13.b $8$ $19.931$ 8.0.134560000.4 None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta _{1}q^{5}-\beta _{6}q^{7}+q^{9}+(\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots\)
2496.2.c.r 2496.c 13.b $8$ $19.931$ 8.0.134560000.4 None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta _{1}q^{5}+\beta _{6}q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2496, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2496, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)