Properties

Label 2025.2.r
Level $2025$
Weight $2$
Character orbit 2025.r
Rep. character $\chi_{2025}(136,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $944$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 2025 = 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2025.r (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 2256 976 1280
Cusp forms 2064 944 1120
Eisenstein series 192 32 160

Trace form

\( 944 q + 122 q^{4} + 16 q^{7} + O(q^{10}) \) \( 944 q + 122 q^{4} + 16 q^{7} - 8 q^{10} + 6 q^{13} + 110 q^{16} - 12 q^{19} - 2 q^{22} + 32 q^{25} - 44 q^{28} - 6 q^{31} - 2 q^{34} + 12 q^{37} - 14 q^{40} + 16 q^{43} + 4 q^{46} - 408 q^{49} + 2 q^{52} - 44 q^{55} + 58 q^{58} + 6 q^{61} - 212 q^{64} + 24 q^{67} - 70 q^{70} - 12 q^{73} - 8 q^{76} + 66 q^{79} - 40 q^{82} + 4 q^{85} + 70 q^{88} - 96 q^{91} - 182 q^{94} + 6 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)