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Properties

Label 3675.2.bo
Level $3675$
Weight $2$
Character orbit 3675.bo
Rep. character $\chi_{3675}(361,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1600$
Sturm bound $1120$

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Defining parameters

Level: \( N \) \(=\) \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3675.bo (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3675, [\chi])\).

Total New Old
Modular forms 4608 1600 3008
Cusp forms 4352 1600 2752
Eisenstein series 256 0 256

Trace form

\( 1600 q + 200 q^{4} + 2 q^{5} + 8 q^{6} + 36 q^{8} + 200 q^{9} + O(q^{10}) \) \( 1600 q + 200 q^{4} + 2 q^{5} + 8 q^{6} + 36 q^{8} + 200 q^{9} + 8 q^{10} - 6 q^{11} - 4 q^{15} + 200 q^{16} + 12 q^{17} - 16 q^{19} + 8 q^{20} - 56 q^{22} + 48 q^{24} - 8 q^{25} - 48 q^{29} - 30 q^{31} + 24 q^{32} + 12 q^{33} - 400 q^{36} - 4 q^{37} - 2 q^{38} + 12 q^{40} + 36 q^{41} + 152 q^{43} + 16 q^{44} + 2 q^{45} + 44 q^{46} + 4 q^{47} - 32 q^{48} + 68 q^{50} + 6 q^{52} - 48 q^{53} - 4 q^{54} - 16 q^{55} + 32 q^{57} + 140 q^{58} - 24 q^{59} - 38 q^{60} - 20 q^{61} + 216 q^{62} - 268 q^{64} + 18 q^{65} - 16 q^{66} - 52 q^{67} + 12 q^{68} + 32 q^{69} + 64 q^{71} - 18 q^{72} - 44 q^{73} + 92 q^{74} + 8 q^{75} - 344 q^{76} + 64 q^{78} - 12 q^{79} - 24 q^{80} + 200 q^{81} - 68 q^{82} + 112 q^{83} + 236 q^{85} + 24 q^{86} + 16 q^{87} - 60 q^{88} + 44 q^{90} + 156 q^{92} + 192 q^{93} - 16 q^{94} + 174 q^{95} - 58 q^{96} + 84 q^{97} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3675, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)