Properties

Label 3630.2.bb
Level $3630$
Weight $2$
Character orbit 3630.bb
Rep. character $\chi_{3630}(329,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $2640$
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.bb (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1815 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 8000 2640 5360
Cusp forms 7840 2640 5200
Eisenstein series 160 0 160

Trace form

\( 2640q + 264q^{4} - 8q^{9} + O(q^{10}) \) \( 2640q + 264q^{4} - 8q^{9} + 22q^{10} - 264q^{16} + 20q^{25} + 8q^{34} + 8q^{36} + 48q^{45} - 136q^{49} - 88q^{51} - 28q^{55} + 264q^{64} - 36q^{66} + 16q^{69} - 4q^{70} + 32q^{75} + 88q^{79} - 56q^{81} + 200q^{91} + 56q^{99} + O(q^{100}) \)

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

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