Properties

Label 3549.2.bn
Level $3549$
Weight $2$
Character orbit 3549.bn
Rep. character $\chi_{3549}(146,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $780$
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.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 1028 860 168
Cusp forms 916 780 136
Eisenstein series 112 80 32

Trace form

\( 780q + 372q^{4} + 5q^{7} + 4q^{9} + O(q^{10}) \) \( 780q + 372q^{4} + 5q^{7} + 4q^{9} + 18q^{15} - 328q^{16} - 8q^{18} + 26q^{21} + 32q^{22} + 628q^{25} - 38q^{28} + 4q^{30} + 14q^{36} + 8q^{37} + 8q^{42} - 14q^{43} + 36q^{46} + 15q^{49} + 52q^{51} + 44q^{57} + 116q^{60} - 7q^{63} - 496q^{64} + 50q^{67} + 64q^{70} - 62q^{72} - 116q^{79} + 24q^{81} + 18q^{84} - 28q^{85} - 80q^{88} - 16q^{93} + 32q^{99} + O(q^{100}) \)

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

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