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Properties

Label 3630.2.c
Level $3630$
Weight $2$
Character orbit 3630.c
Rep. character $\chi_{3630}(2179,\cdot)$
Character field $\Q$
Dimension $110$
Sturm bound $1584$

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Defining parameters

Level: \( N \) \(=\) \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3630.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(1584\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3630, [\chi])\).

Total New Old
Modular forms 840 110 730
Cusp forms 744 110 634
Eisenstein series 96 0 96

Trace form

\( 110 q - 110 q^{4} + 4 q^{5} - 2 q^{6} - 110 q^{9} + O(q^{10}) \) \( 110 q - 110 q^{4} + 4 q^{5} - 2 q^{6} - 110 q^{9} + 2 q^{10} - 4 q^{14} - 2 q^{15} + 110 q^{16} + 16 q^{19} - 4 q^{20} - 12 q^{21} + 2 q^{24} + 10 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} - 4 q^{34} + 28 q^{35} + 110 q^{36} + 4 q^{39} - 2 q^{40} - 36 q^{41} - 4 q^{45} - 8 q^{46} - 102 q^{49} + 24 q^{50} + 4 q^{51} + 2 q^{54} + 4 q^{56} + 20 q^{59} + 2 q^{60} - 52 q^{61} - 110 q^{64} + 44 q^{65} - 8 q^{69} + 40 q^{70} - 72 q^{71} - 4 q^{74} + 24 q^{75} - 16 q^{76} - 16 q^{79} + 4 q^{80} + 110 q^{81} + 12 q^{84} + 44 q^{85} - 24 q^{86} - 4 q^{89} - 2 q^{90} - 24 q^{91} - 16 q^{94} - 2 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3630, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3630, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3630, [\chi]) \cong \)