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Properties

Label 3525.2.bk
Level $3525$
Weight $2$
Character orbit 3525.bk
Rep. character $\chi_{3525}(16,\cdot)$
Character field $\Q(\zeta_{115})$
Dimension $21120$
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.bk (of order \(115\) and degree \(88\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1175 \)
Character field: \(\Q(\zeta_{115})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 42592 21120 21472
Cusp forms 41888 21120 20768
Eisenstein series 704 0 704

Trace form

\( 21120 q + 240 q^{4} + 4 q^{5} + 8 q^{7} - 36 q^{8} + 240 q^{9} + O(q^{10}) \) \( 21120 q + 240 q^{4} + 4 q^{5} + 8 q^{7} - 36 q^{8} + 240 q^{9} + 20 q^{10} - 12 q^{11} + 16 q^{12} + 24 q^{14} + 216 q^{16} - 12 q^{17} + 16 q^{19} + 28 q^{20} + 16 q^{22} - 72 q^{23} + 12 q^{25} + 56 q^{28} - 24 q^{29} + 8 q^{30} + 24 q^{31} + 48 q^{32} + 228 q^{35} + 240 q^{36} + 24 q^{37} + 20 q^{38} + 16 q^{39} - 280 q^{40} + 378 q^{41} + 56 q^{43} - 52 q^{44} + 4 q^{45} - 352 q^{46} + 16 q^{47} + 32 q^{48} - 952 q^{49} - 412 q^{50} - 92 q^{52} - 194 q^{55} + 828 q^{56} + 16 q^{57} - 156 q^{58} + 24 q^{59} + 24 q^{60} - 108 q^{61} + 104 q^{62} - 12 q^{63} + 204 q^{64} + 32 q^{65} + 32 q^{66} - 64 q^{67} + 88 q^{68} + 16 q^{69} + 24 q^{70} - 48 q^{71} - 36 q^{72} - 16 q^{73} + 40 q^{75} - 136 q^{76} + 112 q^{77} + 80 q^{78} + 16 q^{79} - 182 q^{80} + 240 q^{81} - 136 q^{82} - 24 q^{83} - 164 q^{85} + 24 q^{87} - 104 q^{88} - 132 q^{90} + 52 q^{91} + 36 q^{92} - 188 q^{94} - 456 q^{95} - 210 q^{96} + 40 q^{97} - 192 q^{98} + 8 q^{99} + O(q^{100}) \)

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

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