Properties

Label 2640.2.en
Level $2640$
Weight $2$
Character orbit 2640.en
Rep. character $\chi_{2640}(251,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3072$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2640.en (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 528 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2640, [\chi])\).

Total New Old
Modular forms 4672 3072 1600
Cusp forms 4544 3072 1472
Eisenstein series 128 0 128

Trace form

\( 3072 q + O(q^{10}) \) \( 3072 q + 64 q^{16} - 96 q^{22} + 32 q^{24} + 48 q^{28} - 40 q^{42} - 64 q^{46} - 40 q^{48} - 768 q^{49} - 16 q^{52} - 144 q^{54} + 64 q^{58} + 84 q^{60} - 72 q^{64} + 16 q^{66} + 128 q^{67} + 256 q^{76} + 104 q^{78} + 120 q^{82} + 32 q^{84} - 8 q^{88} + 144 q^{91} + 192 q^{94} + 32 q^{96} - 32 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2640, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)