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Properties

Label 3640.2.iw
Level $3640$
Weight $2$
Character orbit 3640.iw
Rep. character $\chi_{3640}(1051,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1344$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.iw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3640, [\chi])\).

Total New Old
Modular forms 2720 1344 1376
Cusp forms 2656 1344 1312
Eisenstein series 64 0 64

Trace form

\( 1344 q - 24 q^{6} - 24 q^{8} - 672 q^{9} + O(q^{10}) \) \( 1344 q - 24 q^{6} - 24 q^{8} - 672 q^{9} - 48 q^{18} + 64 q^{24} + 56 q^{26} - 96 q^{30} + 40 q^{32} - 40 q^{34} + 72 q^{36} + 48 q^{44} - 64 q^{46} + 64 q^{48} + 104 q^{52} + 176 q^{54} + 56 q^{58} - 96 q^{59} + 192 q^{62} - 208 q^{66} + 48 q^{68} - 224 q^{72} + 104 q^{74} - 256 q^{76} - 56 q^{78} - 672 q^{81} + 240 q^{82} - 112 q^{84} + 240 q^{86} - 120 q^{88} - 96 q^{92} - 32 q^{94} + 104 q^{96} + 256 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3640, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)