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Properties

Label 3075.2.dp
Level $3075$
Weight $2$
Character orbit 3075.dp
Rep. character $\chi_{3075}(428,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3328$
Sturm bound $840$

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Defining parameters

Level: \( N \) \(=\) \( 3075 = 3 \cdot 5^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3075.dp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3075 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3075, [\chi])\).

Total New Old
Modular forms 3392 3392 0
Cusp forms 3328 3328 0
Eisenstein series 64 64 0

Trace form

\( 3328 q - 16 q^{3} - 2 q^{6} - 12 q^{7} - 20 q^{9} + O(q^{10}) \) \( 3328 q - 16 q^{3} - 2 q^{6} - 12 q^{7} - 20 q^{9} - 28 q^{10} + 4 q^{12} - 20 q^{13} + 6 q^{15} - 3256 q^{16} + 2 q^{18} - 40 q^{19} - 2 q^{21} + 52 q^{22} + 40 q^{24} + 4 q^{25} + 2 q^{27} + 12 q^{28} + 14 q^{30} - 24 q^{31} + 12 q^{33} + 6 q^{36} - 84 q^{37} + 20 q^{40} - 12 q^{42} + 48 q^{43} + 16 q^{45} - 24 q^{46} + 84 q^{48} - 12 q^{51} + 60 q^{52} - 10 q^{54} - 120 q^{55} - 22 q^{57} - 20 q^{58} + 82 q^{60} - 4 q^{61} - 44 q^{63} + 60 q^{66} + 68 q^{67} - 10 q^{69} + 28 q^{70} + 2 q^{72} - 6 q^{75} - 8 q^{76} - 56 q^{78} - 120 q^{79} - 12 q^{81} - 100 q^{82} - 190 q^{84} - 32 q^{85} - 102 q^{87} - 196 q^{88} - 180 q^{90} - 24 q^{91} + 52 q^{93} - 20 q^{94} - 16 q^{96} + 52 q^{97} + 100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3075, [\chi])\) into newform subspaces

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