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Properties

Label 3025.2.bn
Level $3025$
Weight $2$
Character orbit 3025.bn
Rep. character $\chi_{3025}(118,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1232$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3025.bn (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 2928 1360 1568
Cusp forms 2352 1232 1120
Eisenstein series 576 128 448

Trace form

\( 1232 q - 10 q^{2} - 2 q^{3} + 20 q^{6} - 10 q^{8} + O(q^{10}) \) \( 1232 q - 10 q^{2} - 2 q^{3} + 20 q^{6} - 10 q^{8} + 124 q^{12} - 10 q^{13} + 304 q^{16} - 10 q^{18} + 64 q^{23} + 92 q^{26} - 14 q^{27} + 50 q^{28} - 20 q^{31} + 432 q^{36} - 14 q^{37} + 10 q^{38} + 140 q^{41} + 50 q^{42} - 120 q^{46} - 20 q^{47} - 114 q^{48} + 100 q^{51} - 50 q^{52} - 44 q^{53} - 312 q^{56} + 30 q^{57} - 26 q^{58} - 60 q^{61} + 100 q^{62} - 30 q^{63} + 112 q^{67} - 30 q^{68} - 28 q^{71} + 80 q^{72} + 50 q^{73} + 236 q^{78} + 160 q^{81} - 14 q^{82} + 90 q^{83} - 48 q^{86} + 44 q^{91} - 40 q^{92} - 26 q^{93} + 60 q^{96} - 14 q^{97} + O(q^{100}) \)

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

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