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Properties

Label 3525.2.bo
Level $3525$
Weight $2$
Character orbit 3525.bo
Rep. character $\chi_{3525}(4,\cdot)$
Character field $\Q(\zeta_{230})$
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.bo (of order \(230\) and degree \(88\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1175 \)
Character field: \(\Q(\zeta_{230})\)
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

\( 21120 q - 240 q^{4} + 4 q^{5} + 60 q^{8} - 240 q^{9} + O(q^{10}) \) \( 21120 q - 240 q^{4} + 4 q^{5} + 60 q^{8} - 240 q^{9} - 4 q^{10} + 12 q^{11} + 24 q^{14} + 264 q^{16} - 20 q^{17} + 16 q^{19} - 28 q^{20} + 40 q^{23} - 4 q^{25} - 24 q^{29} + 8 q^{30} - 24 q^{31} + 180 q^{35} + 240 q^{36} - 60 q^{38} + 16 q^{39} - 208 q^{40} - 378 q^{41} - 52 q^{44} - 4 q^{45} + 352 q^{46} - 40 q^{47} + 968 q^{49} - 212 q^{50} - 180 q^{52} + 40 q^{53} - 170 q^{55} - 828 q^{56} - 20 q^{58} + 24 q^{59} - 24 q^{60} + 108 q^{61} + 20 q^{63} - 276 q^{64} - 8 q^{65} - 32 q^{66} + 80 q^{67} + 16 q^{69} - 56 q^{70} + 48 q^{71} + 60 q^{72} + 80 q^{73} + 8 q^{75} + 136 q^{76} + 16 q^{79} + 382 q^{80} + 240 q^{81} - 80 q^{83} + 204 q^{85} - 200 q^{88} + 36 q^{90} - 52 q^{91} + 180 q^{92} + 252 q^{94} + 288 q^{95} - 210 q^{96} - 200 q^{98} + 8 q^{99} + O(q^{100}) \)

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

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