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Properties

Label 3075.2.df
Level $3075$
Weight $2$
Character orbit 3075.df
Rep. character $\chi_{3075}(169,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1696$
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.df (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1025 \)
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 1696 1696
Cusp forms 3328 1696 1632
Eisenstein series 64 0 64

Trace form

\( 1696 q - 432 q^{4} + O(q^{10}) \) \( 1696 q - 432 q^{4} - 24 q^{10} + 36 q^{14} - 4 q^{15} - 448 q^{16} - 80 q^{17} + 8 q^{19} - 60 q^{20} - 40 q^{22} - 48 q^{25} - 36 q^{26} + 72 q^{29} + 24 q^{30} + 48 q^{31} - 36 q^{34} - 4 q^{35} + 60 q^{37} + 32 q^{40} + 24 q^{41} + 60 q^{43} - 16 q^{45} + 40 q^{46} + 80 q^{48} - 32 q^{51} + 120 q^{53} - 80 q^{55} - 48 q^{56} - 40 q^{57} + 100 q^{58} - 96 q^{60} + 80 q^{61} - 80 q^{62} - 492 q^{64} + 140 q^{65} + 64 q^{66} - 8 q^{69} - 68 q^{70} - 48 q^{71} + 8 q^{75} + 56 q^{76} + 240 q^{77} - 8 q^{79} + 60 q^{80} + 424 q^{81} + 60 q^{85} - 240 q^{86} - 80 q^{88} - 120 q^{89} + 60 q^{90} + 60 q^{91} + 200 q^{92} - 40 q^{93} + 24 q^{94} - 44 q^{95} - 60 q^{96} + 60 q^{97} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3075, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3075, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1025, [\chi])\)\(^{\oplus 2}\)