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Properties

Label 690.3.v
Level $690$
Weight $3$
Character orbit 690.v
Rep. character $\chi_{690}(13,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $960$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.v (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(690, [\chi])\).

Total New Old
Modular forms 5920 960 4960
Cusp forms 5600 960 4640
Eisenstein series 320 0 320

Trace form

\( 960 q + 16 q^{5} + 48 q^{7} + O(q^{10}) \) \( 960 q + 16 q^{5} + 48 q^{7} + 32 q^{11} - 16 q^{13} + 384 q^{16} - 112 q^{17} - 32 q^{22} + 192 q^{23} - 208 q^{25} - 128 q^{26} + 432 q^{28} + 96 q^{30} - 16 q^{31} + 144 q^{33} + 176 q^{35} - 576 q^{36} - 576 q^{37} + 128 q^{38} + 144 q^{41} - 96 q^{43} + 32 q^{46} + 528 q^{47} - 64 q^{50} - 96 q^{51} - 32 q^{52} - 352 q^{53} + 32 q^{55} - 128 q^{56} + 864 q^{57} + 96 q^{60} - 1104 q^{61} + 32 q^{62} + 144 q^{63} - 192 q^{65} + 192 q^{66} + 64 q^{67} + 224 q^{68} - 64 q^{70} + 16 q^{71} - 144 q^{73} + 192 q^{75} + 192 q^{76} + 80 q^{77} - 96 q^{78} - 64 q^{80} + 864 q^{81} + 64 q^{82} + 192 q^{83} - 128 q^{85} - 48 q^{87} + 64 q^{88} - 864 q^{91} + 32 q^{92} + 192 q^{93} + 1768 q^{95} - 768 q^{97} + 2304 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(690, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(690, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)