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Properties

Label 3025.2.bp
Level $3025$
Weight $2$
Character orbit 3025.bp
Rep. character $\chi_{3025}(362,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2096$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3025.bp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(660\)

Dimensions

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

Total New Old
Modular forms 2736 2224 512
Cusp forms 2544 2096 448
Eisenstein series 192 128 64

Trace form

\( 2096 q + 12 q^{3} + 20 q^{4} + 12 q^{5} + 20 q^{9} + O(q^{10}) \) \( 2096 q + 12 q^{3} + 20 q^{4} + 12 q^{5} + 20 q^{9} - 44 q^{12} + 20 q^{14} + 8 q^{15} + 488 q^{16} + 36 q^{20} - 44 q^{23} - 20 q^{25} + 32 q^{26} - 36 q^{27} + 12 q^{31} - 80 q^{34} + 488 q^{36} + 24 q^{37} + 60 q^{38} - 40 q^{42} + 72 q^{45} - 80 q^{47} - 76 q^{48} + 24 q^{53} - 16 q^{56} - 184 q^{58} + 40 q^{59} - 52 q^{60} - 140 q^{64} - 92 q^{67} + 20 q^{69} + 164 q^{70} - 28 q^{71} - 112 q^{75} - 136 q^{78} + 132 q^{80} + 368 q^{81} + 144 q^{82} + 12 q^{86} - 180 q^{89} + 12 q^{91} - 80 q^{92} - 124 q^{93} + 244 q^{97} + O(q^{100}) \)

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

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