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Properties

Label 3640.2.oy
Level $3640$
Weight $2$
Character orbit 3640.oy
Rep. character $\chi_{3640}(241,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $448$
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.oy (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 2752 448 2304
Cusp forms 2624 448 2176
Eisenstein series 128 0 128

Trace form

\( 448 q - 16 q^{7} + 224 q^{9} + O(q^{10}) \) \( 448 q - 16 q^{7} + 224 q^{9} - 8 q^{11} + 12 q^{19} + 24 q^{21} + 8 q^{29} - 48 q^{33} - 4 q^{35} - 16 q^{37} - 16 q^{39} - 36 q^{41} + 96 q^{43} - 24 q^{49} - 48 q^{51} + 8 q^{53} + 16 q^{57} + 72 q^{61} - 48 q^{63} + 12 q^{65} - 8 q^{67} + 88 q^{71} - 192 q^{81} - 48 q^{83} - 64 q^{91} + 8 q^{93} - 44 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(455, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(910, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1820, [\chi])\)\(^{\oplus 2}\)