↑

Properties

Label 3025.2.bm
Level $3025$
Weight $2$
Character orbit 3025.bm
Rep. character $\chi_{3025}(602,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2096$
Sturm bound $660$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3025.bm (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

\( 2096 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 12 q^{5} + 10 q^{6} + 10 q^{8} + O(q^{10}) \) \( 2096 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 12 q^{5} + 10 q^{6} + 10 q^{8} + 20 q^{10} - 34 q^{12} + 10 q^{13} + 10 q^{14} - 2 q^{15} + 478 q^{16} + 10 q^{18} - 10 q^{19} + 26 q^{20} - 44 q^{23} + 40 q^{24} + 12 q^{26} - 16 q^{27} - 50 q^{28} + 10 q^{29} + 10 q^{30} + 2 q^{31} + 70 q^{32} - 80 q^{34} + 10 q^{35} + 438 q^{36} - 16 q^{37} - 80 q^{38} + 120 q^{39} + 10 q^{40} + 10 q^{41} - 110 q^{42} - 138 q^{45} + 10 q^{46} + 70 q^{47} + 74 q^{48} + 110 q^{49} + 10 q^{50} + 20 q^{51} + 10 q^{52} + 94 q^{53} - 56 q^{56} - 70 q^{57} - 54 q^{58} - 40 q^{59} + 8 q^{60} - 30 q^{62} - 30 q^{63} - 310 q^{64} - 52 q^{67} - 120 q^{68} - 210 q^{69} - 56 q^{70} + 62 q^{71} - 70 q^{72} + 100 q^{73} + 110 q^{74} - 42 q^{75} + 24 q^{78} - 70 q^{79} + 122 q^{80} - 1612 q^{81} - 246 q^{82} + 110 q^{83} + 70 q^{84} - 30 q^{85} + 2 q^{86} - 30 q^{87} - 80 q^{89} + 170 q^{90} + 2 q^{91} + 130 q^{92} - 34 q^{93} + 80 q^{94} - 70 q^{95} - 86 q^{97} - 80 q^{98} + O(q^{100}) \)

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

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