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Properties

Label 3630.2.bi
Level $3630$
Weight $2$
Character orbit 3630.bi
Rep. character $\chi_{3630}(23,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $5280$
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.bi (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1815 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 16000 5280 10720
Cusp forms 15680 5280 10400
Eisenstein series 320 0 320

Trace form

\( 5280 q + 8 q^{7} + O(q^{10}) \) \( 5280 q + 8 q^{7} + 36 q^{10} + 72 q^{13} + 528 q^{16} - 16 q^{21} - 84 q^{22} - 16 q^{25} + 8 q^{28} - 16 q^{31} + 8 q^{33} + 16 q^{36} - 16 q^{37} - 32 q^{42} - 48 q^{43} + 32 q^{45} + 16 q^{46} - 128 q^{51} + 16 q^{52} + 100 q^{55} + 32 q^{57} + 56 q^{58} + 32 q^{61} + 180 q^{63} - 8 q^{66} - 48 q^{67} - 64 q^{70} + 56 q^{73} - 64 q^{75} - 16 q^{78} - 16 q^{81} - 16 q^{85} + 64 q^{87} + 4 q^{88} - 32 q^{90} - 528 q^{91} + 88 q^{93} + 40 q^{97} + O(q^{100}) \)

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

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