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Properties

Label 3025.2.z
Level $3025$
Weight $2$
Character orbit 3025.z
Rep. character $\chi_{3025}(124,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $616$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3025.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(660\)

Dimensions

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

Total New Old
Modular forms 1464 680 784
Cusp forms 1176 616 560
Eisenstein series 288 64 224

Trace form

\( 616 q + 140 q^{4} - 6 q^{6} + 148 q^{9} + O(q^{10}) \) \( 616 q + 140 q^{4} - 6 q^{6} + 148 q^{9} - 2 q^{14} - 92 q^{16} + 2 q^{19} + 44 q^{21} - 10 q^{24} + 124 q^{26} - 2 q^{29} + 22 q^{31} + 120 q^{34} - 146 q^{36} + 66 q^{39} - 58 q^{41} - 4 q^{46} + 114 q^{49} - 98 q^{51} + 72 q^{54} - 240 q^{56} - 78 q^{59} - 40 q^{61} + 148 q^{64} + 56 q^{69} + 58 q^{71} + 122 q^{74} + 92 q^{76} + 30 q^{79} - 36 q^{81} - 60 q^{84} + 52 q^{86} - 36 q^{89} + 4 q^{91} + 20 q^{94} - 228 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3025, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)