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Properties

Label 3700.2.eb
Level $3700$
Weight $2$
Character orbit 3700.eb
Rep. character $\chi_{3700}(9,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $2256$
Sturm bound $1140$

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Defining parameters

Level: \( N \) \(=\) \( 3700 = 2^{2} \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3700.eb (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 925 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(1140\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3700, [\chi])\).

Total New Old
Modular forms 13824 2256 11568
Cusp forms 13536 2256 11280
Eisenstein series 288 0 288

Trace form

\( 2256 q - 6 q^{9} - 12 q^{11} + 9 q^{15} - 30 q^{25} - 72 q^{31} + 24 q^{35} + 66 q^{41} - 183 q^{45} - 30 q^{55} - 72 q^{59} - 36 q^{61} + 33 q^{65} + 15 q^{67} + 90 q^{69} + 6 q^{71} + 252 q^{75} - 9 q^{81}+ \cdots - 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(3700, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3700, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1850, [\chi])\)\(^{\oplus 2}\)