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Properties

Label 2025.2.bb
Level $2025$
Weight $2$
Character orbit 2025.bb
Rep. character $\chi_{2025}(143,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $624$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 2025 = 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2025.bb (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 3456 672 2784
Cusp forms 3024 624 2400
Eisenstein series 432 48 384

Trace form

\( 624 q - 12 q^{2} + 12 q^{7} - 18 q^{8} + O(q^{10}) \) \( 624 q - 12 q^{2} + 12 q^{7} - 18 q^{8} + 12 q^{13} - 24 q^{16} - 18 q^{17} + 12 q^{22} - 36 q^{23} + 24 q^{28} - 24 q^{31} - 48 q^{32} + 6 q^{37} + 12 q^{38} + 120 q^{41} + 12 q^{43} - 12 q^{46} - 6 q^{47} - 12 q^{52} + 432 q^{56} + 12 q^{58} + 48 q^{61} - 18 q^{62} - 24 q^{67} - 60 q^{68} + 36 q^{71} + 6 q^{73} - 72 q^{76} + 132 q^{77} + 24 q^{82} + 48 q^{83} + 276 q^{86} + 48 q^{88} - 12 q^{91} + 258 q^{92} - 24 q^{97} + 324 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)