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Properties

Label 3025.2.bs
Level $3025$
Weight $2$
Character orbit 3025.bs
Rep. character $\chi_{3025}(199,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1960$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3025.bs (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(660\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3025, [\chi])\).

Total New Old
Modular forms 3360 2000 1360
Cusp forms 3240 1960 1280
Eisenstein series 120 40 80

Trace form

\( 1960 q + 212 q^{4} - 50 q^{6} - 1872 q^{9} + O(q^{10}) \) \( 1960 q + 212 q^{4} - 50 q^{6} - 1872 q^{9} - 48 q^{11} + 18 q^{14} - 184 q^{16} + 10 q^{19} - 72 q^{21} - 108 q^{24} - 30 q^{26} + 14 q^{29} - 26 q^{31} + 26 q^{34} - 386 q^{36} + 92 q^{39} - 14 q^{41} + 24 q^{44} + 2 q^{46} + 110 q^{49} + 10 q^{51} - 56 q^{54} - 100 q^{56} + 2 q^{59} - 2 q^{61} + 180 q^{64} - 96 q^{66} + 112 q^{69} - 106 q^{71} + 30 q^{74} + 28 q^{76} - 66 q^{79} + 1608 q^{81} + 108 q^{84} + 22 q^{86} + 148 q^{89} + 66 q^{91} + 44 q^{94} - 40 q^{96} + 418 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3025, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3025, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)