Properties

Label 525.2.bg
Level 525
Weight 2
Character orbit bg
Rep. character \(\chi_{525}(16,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 320
Newform subspaces 2
Sturm bound 160
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 525.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(160\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(525, [\chi])\).

Total New Old
Modular forms 672 320 352
Cusp forms 608 320 288
Eisenstein series 64 0 64

Trace form

\( 320q + 40q^{4} - 2q^{5} - 8q^{6} + 8q^{7} - 36q^{8} + 40q^{9} + O(q^{10}) \) \( 320q + 40q^{4} - 2q^{5} - 8q^{6} + 8q^{7} - 36q^{8} + 40q^{9} - 8q^{10} + 6q^{11} + 12q^{14} + 4q^{15} + 40q^{16} - 12q^{17} + 16q^{19} - 8q^{20} + 32q^{22} + 12q^{23} - 48q^{24} - 70q^{28} + 24q^{29} + 16q^{30} + 30q^{31} - 24q^{32} - 12q^{33} - 16q^{35} - 80q^{36} - 4q^{37} + 2q^{38} - 12q^{40} - 36q^{41} + 14q^{42} - 136q^{43} - 16q^{44} - 2q^{45} - 32q^{46} - 4q^{47} + 32q^{48} + 16q^{49} - 148q^{50} - 6q^{52} - 60q^{53} + 4q^{54} + 16q^{55} - 16q^{57} - 24q^{58} + 24q^{59} + 26q^{60} + 20q^{61} - 216q^{62} - 14q^{63} - 164q^{64} + 10q^{65} + 16q^{66} + 36q^{67} - 12q^{68} - 32q^{69} - 32q^{71} + 18q^{72} + 44q^{73} - 12q^{74} - 8q^{75} + 344q^{76} - 28q^{77} - 16q^{78} + 4q^{79} + 24q^{80} + 40q^{81} + 68q^{82} - 112q^{83} + 48q^{84} + 132q^{85} - 24q^{86} - 16q^{87} + 72q^{88} - 44q^{90} - 26q^{91} - 92q^{92} - 96q^{93} + 16q^{94} - 102q^{95} + 58q^{96} - 84q^{97} + 192q^{98} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
525.2.bg.a \(160\) \(4.192\) None \(-2\) \(-20\) \(0\) \(4\)
525.2.bg.b \(160\) \(4.192\) None \(2\) \(20\) \(-2\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database