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Properties

Label 3525.2.g
Level $3525$
Weight $2$
Character orbit 3525.g
Rep. character $\chi_{3525}(3524,\cdot)$
Character field $\Q$
Dimension $284$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3525.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 705 \)
Character field: \(\Q\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3525, [\chi])\).

Total New Old
Modular forms 492 292 200
Cusp forms 468 284 184
Eisenstein series 24 8 16

Trace form

\( 284 q + 280 q^{4} + 12 q^{6} + 8 q^{9} + O(q^{10}) \) \( 284 q + 280 q^{4} + 12 q^{6} + 8 q^{9} + 288 q^{16} - 40 q^{21} + 24 q^{24} - 72 q^{34} - 4 q^{36} - 236 q^{49} - 20 q^{51} - 20 q^{54} - 104 q^{61} + 336 q^{64} - 8 q^{79} + 40 q^{81} + 40 q^{84} - 24 q^{94} - 12 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3525, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3525, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(705, [\chi])\)\(^{\oplus 2}\)