Properties

Label 3549.2.p
Level $3549$
Weight $2$
Character orbit 3549.p
Rep. character $\chi_{3549}(1084,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $408$
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.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 1024 408 616
Cusp forms 912 408 504
Eisenstein series 112 0 112

Trace form

\( 408q - 4q^{7} - 408q^{9} + O(q^{10}) \) \( 408q - 4q^{7} - 408q^{9} - 16q^{11} + 16q^{14} - 384q^{16} - 12q^{21} - 32q^{22} - 4q^{28} - 16q^{29} - 40q^{32} + 16q^{35} + 24q^{42} - 16q^{44} + 8q^{46} - 40q^{50} + 112q^{53} - 40q^{57} - 48q^{58} + 16q^{60} + 4q^{63} + 56q^{67} + 16q^{70} - 24q^{71} + 32q^{74} - 48q^{79} + 408q^{81} - 36q^{84} + 40q^{85} - 48q^{86} - 208q^{92} - 40q^{93} - 120q^{98} + 16q^{99} + O(q^{100}) \)

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

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