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Properties

Label 2025.2.e
Level $2025$
Weight $2$
Character orbit 2025.e
Rep. character $\chi_{2025}(676,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $146$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 2025 = 3^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2025.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 612 158 454
Cusp forms 468 146 322
Eisenstein series 144 12 132

Trace form

\( 146 q - 72 q^{4} - 7 q^{7} + O(q^{10}) \) \( 146 q - 72 q^{4} - 7 q^{7} - 7 q^{13} - 62 q^{16} + 2 q^{19} + 68 q^{28} - 20 q^{31} + 46 q^{34} + 26 q^{37} - 16 q^{43} - 40 q^{46} - 74 q^{49} - 16 q^{52} + 42 q^{58} - 5 q^{61} + 4 q^{64} - q^{67} - 34 q^{73} + 54 q^{76} + 11 q^{79} - 48 q^{82} + 48 q^{88} + 78 q^{91} + 76 q^{94} + 11 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)