Properties

Label 3549.2.g
Level $3549$
Weight $2$
Character orbit 3549.g
Rep. character $\chi_{3549}(3548,\cdot)$
Character field $\Q$
Dimension $392$
Sturm bound $970$

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Defining parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q\)
Sturm bound: \(970\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3549, [\chi])\).

Total New Old
Modular forms 512 432 80
Cusp forms 456 392 64
Eisenstein series 56 40 16

Trace form

\( 392q + 384q^{4} + O(q^{10}) \) \( 392q + 384q^{4} + 368q^{16} - 312q^{25} - 52q^{30} + 52q^{36} + 52q^{42} - 48q^{43} + 36q^{49} + 4q^{51} + 336q^{64} - 136q^{79} + 32q^{81} + 96q^{88} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3549, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3549, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)