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Properties

Label 3640.2.bj
Level $3640$
Weight $2$
Character orbit 3640.bj
Rep. character $\chi_{3640}(81,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $224$
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.bj (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 1376 224 1152
Cusp forms 1312 224 1088
Eisenstein series 64 0 64

Trace form

\( 224 q - 16 q^{3} + 8 q^{7} + 224 q^{9} + O(q^{10}) \) \( 224 q - 16 q^{3} + 8 q^{7} + 224 q^{9} + 4 q^{11} - 4 q^{13} - 12 q^{17} + 20 q^{19} - 8 q^{21} - 112 q^{25} - 64 q^{27} + 4 q^{29} + 16 q^{31} + 16 q^{33} - 4 q^{35} - 8 q^{37} - 16 q^{39} - 12 q^{41} + 24 q^{43} - 12 q^{47} + 10 q^{49} - 4 q^{51} - 20 q^{53} + 16 q^{57} - 8 q^{59} + 40 q^{61} - 24 q^{63} + 12 q^{65} - 24 q^{67} + 24 q^{69} - 28 q^{71} + 4 q^{73} + 8 q^{75} + 56 q^{77} + 4 q^{79} + 208 q^{81} + 16 q^{83} + 8 q^{87} - 12 q^{89} - 12 q^{91} + 44 q^{93} - 8 q^{97} + 44 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 6}\)