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Properties

Label 3675.2.bi
Level $3675$
Weight $2$
Character orbit 3675.bi
Rep. character $\chi_{3675}(524,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1992$
Sturm bound $1120$

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Defining parameters

Level: \( N \) \(=\) \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3675.bi (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 735 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3675, [\chi])\).

Total New Old
Modular forms 3432 2040 1392
Cusp forms 3288 1992 1296
Eisenstein series 144 48 96

Trace form

\( 1992 q - 308 q^{4} - 42 q^{6} + 30 q^{9} + O(q^{10}) \) \( 1992 q - 308 q^{4} - 42 q^{6} + 30 q^{9} - 356 q^{16} + 4 q^{21} + 14 q^{24} + 140 q^{34} + 86 q^{36} + 42 q^{39} - 116 q^{46} + 50 q^{49} + 26 q^{51} + 14 q^{54} - 14 q^{61} - 252 q^{64} - 210 q^{66} + 14 q^{69} + 420 q^{76} + 72 q^{79} + 98 q^{81} - 118 q^{84} + 142 q^{91} - 196 q^{94} + 210 q^{96} + 252 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3675, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)