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Properties

Label 2025.2.bk
Level $2025$
Weight $2$
Character orbit 2025.bk
Rep. character $\chi_{2025}(19,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $2112$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 2025 = 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2025.bk (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 675 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 6624 2208 4416
Cusp forms 6336 2112 4224
Eisenstein series 288 96 192

Trace form

\( 2112 q + 30 q^{2} - 18 q^{4} + 36 q^{5} + 15 q^{8} + O(q^{10}) \) \( 2112 q + 30 q^{2} - 18 q^{4} + 36 q^{5} + 15 q^{8} - 12 q^{10} + 18 q^{11} - 30 q^{13} + 18 q^{14} - 6 q^{16} + 15 q^{17} - 9 q^{19} - 27 q^{20} - 30 q^{22} + 30 q^{23} + 12 q^{25} - 192 q^{26} - 60 q^{28} + 18 q^{29} - 6 q^{34} + 3 q^{35} - 15 q^{37} + 30 q^{38} - 21 q^{40} + 18 q^{41} + 69 q^{44} - 9 q^{46} + 105 q^{47} - 48 q^{49} + 114 q^{50} - 90 q^{52} + 60 q^{53} - 48 q^{55} + 105 q^{56} - 30 q^{58} + 9 q^{59} - 18 q^{61} + 15 q^{62} - 231 q^{64} + 75 q^{65} + 60 q^{67} - 102 q^{70} - 75 q^{71} - 15 q^{73} + 78 q^{74} - 72 q^{76} + 270 q^{77} - 18 q^{79} + 90 q^{80} + 30 q^{83} - 9 q^{85} - 42 q^{86} - 30 q^{88} + 111 q^{89} - 9 q^{91} - 330 q^{92} - 18 q^{94} + 117 q^{95} - 30 q^{97} + 15 q^{98} + O(q^{100}) \)

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

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