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
Newforms 2
Sturm bound 160
Trace bound 2

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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: \(\Q(\zeta_{15})\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) into irreducible Hecke orbits

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

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