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Properties

Label 3525.2.bi
Level $3525$
Weight $2$
Character orbit 3525.bi
Rep. character $\chi_{3525}(32,\cdot)$
Character field $\Q(\zeta_{92})$
Dimension $12496$
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.bi (of order \(92\) and degree \(44\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 705 \)
Character field: \(\Q(\zeta_{92})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 21648 12848 8800
Cusp forms 20592 12496 8096
Eisenstein series 1056 352 704

Trace form

\( 12496 q + 46 q^{3} - 68 q^{6} + 84 q^{7} + O(q^{10}) \) \( 12496 q + 46 q^{3} - 68 q^{6} + 84 q^{7} + 46 q^{12} + 84 q^{13} + 360 q^{16} + 34 q^{18} - 68 q^{21} + 84 q^{22} + 34 q^{27} + 100 q^{28} - 168 q^{31} + 26 q^{33} - 100 q^{36} + 60 q^{37} + 6 q^{42} + 84 q^{43} - 320 q^{46} + 68 q^{48} - 132 q^{51} + 148 q^{52} + 106 q^{57} + 20 q^{58} - 136 q^{61} + 70 q^{63} - 132 q^{66} + 124 q^{67} + 34 q^{72} + 148 q^{73} - 16 q^{76} + 122 q^{78} + 84 q^{81} - 12 q^{82} - 30 q^{87} + 68 q^{88} + 1272 q^{91} + 136 q^{93} - 180 q^{96} + 100 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(705, [\chi])\)\(^{\oplus 2}\)