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Properties

Label 3525.2.q
Level $3525$
Weight $2$
Character orbit 3525.q
Rep. character $\chi_{3525}(1129,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $928$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3525.q (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3525, [\chi])\).

Total New Old
Modular forms 1936 928 1008
Cusp forms 1904 928 976
Eisenstein series 32 0 32

Trace form

\( 928 q + 236 q^{4} - 4 q^{5} - 4 q^{6} + 232 q^{9} + O(q^{10}) \) \( 928 q + 236 q^{4} - 4 q^{5} - 4 q^{6} + 232 q^{9} + 4 q^{10} - 244 q^{16} - 12 q^{19} - 12 q^{20} - 8 q^{21} + 60 q^{22} - 48 q^{24} + 24 q^{25} - 24 q^{26} - 60 q^{28} - 8 q^{29} + 32 q^{30} + 12 q^{31} - 20 q^{33} + 72 q^{34} - 16 q^{35} - 236 q^{36} + 20 q^{37} - 88 q^{40} - 8 q^{41} + 20 q^{42} + 4 q^{45} - 16 q^{46} - 968 q^{49} - 12 q^{50} + 64 q^{51} + 100 q^{52} - 60 q^{53} + 4 q^{54} + 12 q^{55} - 48 q^{59} + 84 q^{60} - 16 q^{61} + 20 q^{62} + 260 q^{64} + 148 q^{65} + 8 q^{69} - 4 q^{70} - 32 q^{71} - 40 q^{73} + 104 q^{74} - 8 q^{75} - 72 q^{76} + 80 q^{77} + 24 q^{79} - 60 q^{80} - 232 q^{81} + 60 q^{83} - 24 q^{84} + 20 q^{85} + 72 q^{86} - 80 q^{87} + 280 q^{88} - 36 q^{89} - 4 q^{90} - 200 q^{92} + 16 q^{94} + 160 q^{95} + 32 q^{96} - 80 q^{97} + 80 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3525, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3525, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1175, [\chi])\)\(^{\oplus 2}\)