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Properties

Label 2025.2.bd
Level $2025$
Weight $2$
Character orbit 2025.bd
Rep. character $\chi_{2025}(46,\cdot)$
Character field $\Q(\zeta_{45})$
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.bd (of order \(45\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 675 \)
Character field: \(\Q(\zeta_{45})\)
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

\( 2112 q + 18 q^{2} - 18 q^{4} + 12 q^{5} - 48 q^{7} + 9 q^{8} + O(q^{10}) \) \( 2112 q + 18 q^{2} - 18 q^{4} + 12 q^{5} - 48 q^{7} + 9 q^{8} - 12 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 30 q^{16} + 9 q^{17} - 9 q^{19} + 27 q^{20} - 18 q^{22} + 42 q^{23} + 12 q^{25} + 384 q^{26} - 36 q^{28} + 18 q^{29} - 36 q^{31} + 132 q^{32} - 30 q^{34} + 3 q^{35} - 9 q^{37} + 66 q^{38} - 51 q^{40} + 18 q^{41} - 48 q^{43} + 69 q^{44} - 9 q^{46} - 3 q^{47} - 48 q^{49} - 18 q^{50} - 54 q^{52} + 96 q^{53} - 48 q^{55} - 69 q^{56} - 18 q^{58} + 9 q^{59} - 18 q^{61} + 9 q^{62} + 213 q^{64} + 45 q^{65} - 72 q^{67} - 216 q^{68} + 54 q^{70} + 93 q^{71} - 9 q^{73} + 102 q^{74} - 72 q^{76} + 210 q^{77} - 18 q^{79} + 186 q^{80} - 96 q^{82} + 78 q^{83} - 39 q^{85} + 78 q^{86} - 78 q^{88} + 51 q^{89} - 9 q^{91} + 360 q^{92} - 18 q^{94} + 21 q^{95} + 18 q^{97} - 105 q^{98} + O(q^{100}) \)

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

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