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Properties

Label 3630.2.bv
Level $3630$
Weight $2$
Character orbit 3630.bv
Rep. character $\chi_{3630}(7,\cdot)$
Character field $\Q(\zeta_{220})$
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.bv (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{220})\)
Sturm bound: \(1584\)

Dimensions

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

Total New Old
Modular forms 64000 10560 53440
Cusp forms 62720 10560 52160
Eisenstein series 1280 0 1280

Trace form

\( 10560 q - 16 q^{5} - 40 q^{7} + O(q^{10}) \) \( 10560 q - 16 q^{5} - 40 q^{7} + 44 q^{10} + 8 q^{11} + 88 q^{13} - 12 q^{15} - 264 q^{16} - 40 q^{17} + 84 q^{22} + 16 q^{23} - 40 q^{25} + 16 q^{26} - 20 q^{28} + 16 q^{31} - 12 q^{33} - 264 q^{36} - 232 q^{37} - 40 q^{41} + 12 q^{42} + 40 q^{46} + 88 q^{47} + 80 q^{50} + 80 q^{51} + 40 q^{52} + 72 q^{53} + 28 q^{55} - 16 q^{56} + 80 q^{57} + 12 q^{58} + 24 q^{60} + 80 q^{61} + 80 q^{62} + 40 q^{63} + 32 q^{66} + 336 q^{67} + 40 q^{68} + 12 q^{70} - 20 q^{73} + 32 q^{75} - 88 q^{76} - 24 q^{80} + 2640 q^{81} + 32 q^{82} + 192 q^{85} + 32 q^{86} - 4 q^{88} + 40 q^{91} + 72 q^{92} - 24 q^{93} + 40 q^{95} + 96 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1815, [\chi])\)\(^{\oplus 2}\)