Properties

Label 3630.2.p
Level $3630$
Weight $2$
Character orbit 3630.p
Rep. character $\chi_{3630}(239,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $864$
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.p (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 3360 864 2496
Cusp forms 2976 864 2112
Eisenstein series 384 0 384

Trace form

\( 864q + 216q^{4} - 4q^{9} + O(q^{10}) \) \( 864q + 216q^{4} - 4q^{9} - 8q^{15} - 216q^{16} + 44q^{25} + 30q^{30} + 28q^{31} - 8q^{34} - 16q^{36} - 20q^{39} + 10q^{40} - 48q^{45} + 20q^{46} - 96q^{49} + 20q^{51} + 8q^{60} + 40q^{61} + 216q^{64} + 72q^{69} - 14q^{70} + 48q^{75} + 20q^{79} - 84q^{81} + 20q^{84} + 60q^{85} + 90q^{90} - 24q^{91} + 80q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1815, [\chi])\)\(^{\oplus 2}\)