Properties

Label 3549.2.by
Level $3549$
Weight $2$
Character orbit 3549.by
Rep. character $\chi_{3549}(1441,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $824$
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.by (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 2056 824 1232
Cusp forms 1832 824 1008
Eisenstein series 224 0 224

Trace form

\( 824q + 2q^{7} + 412q^{9} + O(q^{10}) \) \( 824q + 2q^{7} + 412q^{9} + 16q^{11} - 64q^{14} + 424q^{16} + 10q^{21} + 32q^{22} + 56q^{28} + 16q^{29} + 40q^{32} + 8q^{35} + 28q^{37} + 12q^{42} + 12q^{43} + 16q^{44} + 112q^{46} + 30q^{49} - 176q^{50} + 224q^{53} + 180q^{56} - 48q^{57} - 48q^{58} + 104q^{60} + 4q^{63} - 16q^{67} + 56q^{70} + 24q^{71} + 16q^{74} - 96q^{79} - 412q^{81} - 20q^{84} + 56q^{85} + 48q^{86} - 216q^{88} + 16q^{92} - 12q^{93} - 96q^{95} - 36q^{98} - 16q^{99} + O(q^{100}) \)

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

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