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Properties

Label 3525.2.m
Level $3525$
Weight $2$
Character orbit 3525.m
Rep. character $\chi_{3525}(706,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $912$
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.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1936 912 1024
Cusp forms 1904 912 992
Eisenstein series 32 0 32

Trace form

\( 912 q + 4 q^{2} - 224 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} + 12 q^{8} - 228 q^{9} + O(q^{10}) \) \( 912 q + 4 q^{2} - 224 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} + 12 q^{8} - 228 q^{9} + 8 q^{10} + 24 q^{13} + 8 q^{15} - 216 q^{16} + 32 q^{17} - 16 q^{18} - 12 q^{19} - 60 q^{20} + 8 q^{21} - 76 q^{22} - 48 q^{24} + 20 q^{25} + 64 q^{26} - 4 q^{28} + 32 q^{29} - 96 q^{30} - 12 q^{31} - 72 q^{32} + 12 q^{33} + 12 q^{34} + 16 q^{35} - 224 q^{36} - 8 q^{37} + 32 q^{38} - 20 q^{40} + 48 q^{41} + 28 q^{42} - 120 q^{43} + 8 q^{45} + 16 q^{46} + 32 q^{48} + 872 q^{49} + 56 q^{50} - 64 q^{51} + 12 q^{52} - 72 q^{53} + 4 q^{54} + 28 q^{55} + 16 q^{57} + 80 q^{58} - 48 q^{59} - 12 q^{60} + 56 q^{61} - 132 q^{62} + 8 q^{63} - 200 q^{64} - 56 q^{65} + 64 q^{67} + 160 q^{68} + 8 q^{69} + 116 q^{70} + 32 q^{71} + 12 q^{72} + 64 q^{73} + 144 q^{74} + 8 q^{75} + 72 q^{76} + 24 q^{79} + 168 q^{80} - 228 q^{81} + 128 q^{82} + 76 q^{83} - 24 q^{84} - 16 q^{85} - 72 q^{86} - 40 q^{87} - 40 q^{88} - 96 q^{89} + 8 q^{90} - 80 q^{92} - 176 q^{93} + 16 q^{94} - 104 q^{95} - 32 q^{96} - 40 q^{97} + 108 q^{98} + O(q^{100}) \)

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

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