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Properties

Label 2496.2.x
Level $2496$
Weight $2$
Character orbit 2496.x
Rep. character $\chi_{2496}(625,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $2$
Sturm bound $896$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2496.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(896\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 928 96 832
Cusp forms 864 96 768
Eisenstein series 64 0 64

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 16 q^{11} - 16 q^{15} - 16 q^{19} + 32 q^{29} + 48 q^{31} + 48 q^{35} + 32 q^{37} - 96 q^{49} + 16 q^{51} - 32 q^{53} - 32 q^{61} + 16 q^{63} - 32 q^{67} - 32 q^{69} + 16 q^{75} - 32 q^{77} + 32 q^{79} - 96 q^{81} + 32 q^{85} - 96 q^{95} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.x.a 2496.x 16.e $40$ $19.931$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
2496.2.x.b 2496.x 16.e $56$ $19.931$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(2496, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)