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Properties

Label 2025.2.bn
Level $2025$
Weight $2$
Character orbit 2025.bn
Rep. character $\chi_{2025}(32,\cdot)$
Character field $\Q(\zeta_{108})$
Dimension $5760$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 2025 = 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2025.bn (of order \(108\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 405 \)
Character field: \(\Q(\zeta_{108})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2025, [\chi])\).

Total New Old
Modular forms 9936 5904 4032
Cusp forms 9504 5760 3744
Eisenstein series 432 144 288

Trace form

\( 5760 q + 36 q^{2} + 36 q^{3} - 72 q^{6} + 36 q^{7} + 36 q^{8} + O(q^{10}) \) \( 5760 q + 36 q^{2} + 36 q^{3} - 72 q^{6} + 36 q^{7} + 36 q^{8} - 72 q^{11} + 36 q^{12} + 36 q^{13} - 72 q^{16} + 36 q^{17} + 36 q^{18} - 72 q^{21} + 36 q^{22} + 36 q^{23} - 108 q^{26} + 36 q^{27} + 18 q^{28} - 72 q^{31} + 36 q^{32} + 36 q^{33} - 72 q^{36} + 36 q^{37} + 36 q^{38} + 36 q^{42} + 36 q^{43} - 72 q^{46} + 36 q^{47} + 36 q^{48} - 180 q^{51} + 72 q^{52} + 54 q^{53} + 432 q^{56} + 36 q^{57} + 36 q^{58} - 72 q^{61} + 36 q^{62} + 36 q^{63} + 216 q^{66} + 90 q^{67} + 36 q^{68} - 72 q^{71} - 396 q^{72} + 36 q^{73} - 72 q^{76} - 252 q^{77} + 90 q^{78} - 72 q^{81} + 72 q^{82} + 36 q^{83} - 72 q^{86} - 252 q^{87} + 36 q^{88} - 72 q^{91} - 396 q^{92} + 216 q^{93} - 72 q^{96} + 90 q^{97} + 378 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2025, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2025, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)