Properties

Label 3549.2.e
Level $3549$
Weight $2$
Character orbit 3549.e
Rep. character $\chi_{3549}(3212,\cdot)$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 512 436 76
Cusp forms 456 392 64
Eisenstein series 56 44 12

Trace form

\( 392q - 368q^{4} - 4q^{7} + 8q^{9} + O(q^{10}) \) \( 392q - 368q^{4} - 4q^{7} + 8q^{9} + 12q^{15} + 336q^{16} + 20q^{18} + 4q^{21} + 16q^{22} + 328q^{25} + 28q^{28} + 20q^{30} - 44q^{36} - 24q^{37} + 4q^{42} - 32q^{43} + 24q^{46} + 20q^{49} + 20q^{51} - 32q^{57} - 24q^{58} + 28q^{60} - 8q^{63} - 304q^{64} + 32q^{67} + 8q^{70} - 64q^{72} - 24q^{79} - 48q^{81} + 48q^{84} + 16q^{85} - 64q^{88} + 52q^{93} - 20q^{99} + O(q^{100}) \)

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

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