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Properties

Label 2025.2.h
Level $2025$
Weight $2$
Character orbit 2025.h
Rep. character $\chi_{2025}(406,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $464$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 2025 = 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2025.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1128 496 632
Cusp forms 1032 464 568
Eisenstein series 96 32 64

Trace form

\( 464 q - 106 q^{4} + 16 q^{7} + O(q^{10}) \) \( 464 q - 106 q^{4} + 16 q^{7} - 14 q^{10} + 18 q^{13} - 106 q^{16} - 12 q^{19} + 22 q^{22} + 38 q^{25} + 4 q^{28} - 6 q^{31} - 20 q^{34} - 78 q^{37} + 16 q^{40} + 40 q^{43} - 20 q^{46} + 408 q^{49} + 86 q^{52} - 32 q^{55} + 10 q^{58} + 42 q^{61} - 104 q^{64} + 24 q^{67} + 164 q^{70} + 24 q^{73} + 88 q^{76} - 18 q^{79} + 56 q^{82} - 110 q^{85} - 50 q^{88} + 30 q^{91} + 94 q^{94} + 18 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)