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Properties

Label 2496.2.bm
Level $2496$
Weight $2$
Character orbit 2496.bm
Rep. character $\chi_{2496}(785,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
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.bm (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 624 \)
Character field: \(\Q(i)\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 928 232 696
Cusp forms 864 216 648
Eisenstein series 64 16 48

Trace form

\( 216 q + 4 q^{3} + O(q^{10}) \) \( 216 q + 4 q^{3} - 4 q^{13} + 4 q^{15} + 8 q^{19} + 8 q^{21} + 184 q^{25} + 4 q^{27} + 8 q^{31} - 4 q^{33} - 8 q^{37} - 16 q^{43} - 24 q^{45} - 12 q^{57} - 8 q^{61} - 24 q^{63} + 8 q^{67} + 20 q^{75} + 16 q^{79} - 8 q^{81} - 48 q^{85} - 64 q^{93} - 8 q^{97} + O(q^{100}) \)

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

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