Properties

Label 3549.2.ba
Level $3549$
Weight $2$
Character orbit 3549.ba
Rep. character $\chi_{3549}(1013,\cdot)$
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.ba (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

\( 780q + 6q^{3} - 364q^{4} + 6q^{9} + O(q^{10}) \) \( 780q + 6q^{3} - 364q^{4} + 6q^{9} + 12q^{10} - 6q^{12} - 312q^{16} + 24q^{22} + 310q^{25} + 4q^{30} - 88q^{36} + 36q^{40} - 46q^{42} + 20q^{43} + 14q^{49} - 34q^{51} - 24q^{61} + 512q^{64} - 156q^{66} + 114q^{75} - 18q^{79} - 50q^{81} + 24q^{82} + 48q^{87} - 12q^{88} - 168q^{94} + O(q^{100}) \)

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

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