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Properties

Label 2496.2.dq
Level $2496$
Weight $2$
Character orbit 2496.dq
Rep. character $\chi_{2496}(977,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $432$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2496.dq (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 624 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 1856 464 1392
Cusp forms 1728 432 1296
Eisenstein series 128 32 96

Trace form

\( 432 q + 2 q^{3} + O(q^{10}) \) \( 432 q + 2 q^{3} - 8 q^{13} + 8 q^{15} + 4 q^{19} - 20 q^{21} + 368 q^{25} + 8 q^{27} + 16 q^{31} - 8 q^{33} - 4 q^{37} + 28 q^{43} - 12 q^{45} - 24 q^{49} + 120 q^{55} + 12 q^{57} - 4 q^{61} + 36 q^{63} + 4 q^{67} - 6 q^{69} + 34 q^{75} + 32 q^{79} - 4 q^{81} - 24 q^{85} + 12 q^{91} + 40 q^{93} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

The newforms in this space have not yet been added to the LMFDB.

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

\( S_{2}^{\mathrm{old}}(2496, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)