Properties

Label 3549.2.bj
Level $3549$
Weight $2$
Character orbit 3549.bj
Rep. character $\chi_{3549}(844,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $412$
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.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 412 616
Cusp forms 916 412 504
Eisenstein series 112 0 112

Trace form

\( 412q - 2q^{3} + 208q^{4} - 206q^{9} + O(q^{10}) \) \( 412q - 2q^{3} + 208q^{4} - 206q^{9} + 8q^{10} + 4q^{12} - 32q^{14} - 196q^{16} + 8q^{17} - 8q^{22} - 8q^{23} + 202q^{25} + 4q^{27} + 32q^{35} - 416q^{36} + 48q^{38} - 44q^{40} - 8q^{42} + 20q^{43} + 16q^{48} + 74q^{49} + 16q^{51} - 48q^{53} + 104q^{55} - 120q^{56} - 40q^{61} + 224q^{62} - 304q^{64} - 16q^{66} - 4q^{68} - 48q^{69} + 24q^{74} + 30q^{75} - 20q^{77} + 10q^{79} - 206q^{81} - 36q^{87} + 24q^{88} - 16q^{90} - 64q^{92} - 8q^{94} - 40q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)