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Properties

Label 3744.2.ee
Level $3744$
Weight $2$
Character orbit 3744.ee
Rep. character $\chi_{3744}(181,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $1112$
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.ee (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 416 \)
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 1128 1592
Cusp forms 2656 1112 1544
Eisenstein series 64 16 48

Trace form

\( 1112 q - 8 q^{4} + O(q^{10}) \) \( 1112 q - 8 q^{4} - 8 q^{10} - 4 q^{13} + 40 q^{14} - 8 q^{16} - 24 q^{22} + 8 q^{23} - 8 q^{25} + 24 q^{26} + 8 q^{29} + 8 q^{35} - 32 q^{38} + 32 q^{40} - 8 q^{43} + 4 q^{52} + 8 q^{53} + 24 q^{55} + 48 q^{56} - 8 q^{61} - 8 q^{62} - 8 q^{64} + 8 q^{65} - 48 q^{68} + 8 q^{74} + 8 q^{77} + 72 q^{82} - 88 q^{88} - 52 q^{91} - 64 q^{92} - 72 q^{94} - 112 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3744, [\chi]) \cong \)