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

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

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

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