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Properties

Label 3744.2.eg
Level $3744$
Weight $2$
Character orbit 3744.eg
Rep. character $\chi_{3744}(469,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $960$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3744.eg (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3744, [\chi])\).

Total New Old
Modular forms 2720 960 1760
Cusp forms 2656 960 1696
Eisenstein series 64 0 64

Trace form

\( 960 q + O(q^{10}) \) \( 960 q + 16 q^{10} - 8 q^{16} + 24 q^{22} - 16 q^{23} - 48 q^{31} - 48 q^{35} + 56 q^{38} + 64 q^{40} - 16 q^{43} + 96 q^{44} + 24 q^{50} - 32 q^{53} - 32 q^{55} + 96 q^{56} + 64 q^{58} + 64 q^{61} + 24 q^{62} - 120 q^{64} + 16 q^{67} - 32 q^{68} - 32 q^{74} + 32 q^{76} - 32 q^{77} - 56 q^{80} - 80 q^{82} + 80 q^{83} - 88 q^{88} - 160 q^{92} - 152 q^{94} - 216 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)