Properties

Label 3549.2.c
Level $3549$
Weight $2$
Character orbit 3549.c
Rep. character $\chi_{3549}(337,\cdot)$
Character field $\Q$
Dimension $152$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
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 512 152 360
Cusp forms 456 152 304
Eisenstein series 56 0 56

Trace form

\( 152q - 148q^{4} + 152q^{9} + O(q^{10}) \) \( 152q - 148q^{4} + 152q^{9} - 16q^{10} - 16q^{12} + 156q^{16} - 16q^{17} + 48q^{22} - 120q^{25} + 16q^{29} - 8q^{30} + 8q^{35} - 148q^{36} - 56q^{38} + 8q^{40} - 4q^{42} - 40q^{43} + 64q^{48} - 152q^{49} + 24q^{51} + 32q^{53} + 16q^{55} + 8q^{61} + 32q^{62} - 228q^{64} + 64q^{68} - 8q^{69} - 72q^{74} - 32q^{75} + 16q^{77} + 16q^{79} + 152q^{81} - 40q^{82} - 16q^{87} - 48q^{88} - 16q^{90} + 24q^{92} + 80q^{94} + 48q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)