Properties

Label 3630.2.bp
Level $3630$
Weight $2$
Character orbit 3630.bp
Rep. character $\chi_{3630}(29,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $10560$
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.bp (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1815 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 32000 10560 21440
Cusp forms 31360 10560 20800
Eisenstein series 640 0 640

Trace form

\( 10560q - 264q^{4} - 12q^{9} + O(q^{10}) \) \( 10560q - 264q^{4} - 12q^{9} - 22q^{10} + 264q^{16} + 20q^{25} + 30q^{30} - 20q^{31} - 8q^{34} - 8q^{36} - 20q^{39} + 10q^{40} - 48q^{45} + 20q^{46} + 296q^{49} + 108q^{51} + 68q^{55} + 40q^{61} - 264q^{64} - 44q^{66} + 24q^{69} + 14q^{70} + 48q^{75} - 68q^{79} - 124q^{81} + 20q^{84} + 60q^{85} + 90q^{90} - 320q^{91} + 80q^{94} + 124q^{99} + O(q^{100}) \)

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

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