Properties

Label 507.2.s
Level $507$
Weight $2$
Character orbit 507.s
Rep. character $\chi_{507}(5,\cdot)$
Character field $\Q(\zeta_{52})$
Dimension $1392$
Newform subspaces $1$
Sturm bound $121$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.s (of order \(52\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 507 \)
Character field: \(\Q(\zeta_{52})\)
Newform subspaces: \( 1 \)
Sturm bound: \(121\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(507, [\chi])\).

Total New Old
Modular forms 1488 1488 0
Cusp forms 1392 1392 0
Eisenstein series 96 96 0

Trace form

\( 1392q - 22q^{3} - 52q^{4} - 22q^{6} - 56q^{7} - 22q^{9} + O(q^{10}) \) \( 1392q - 22q^{3} - 52q^{4} - 22q^{6} - 56q^{7} - 22q^{9} - 52q^{10} - 26q^{12} - 44q^{13} - 34q^{15} + 48q^{16} - 34q^{18} - 56q^{19} - 22q^{21} - 96q^{22} - 194q^{24} - 52q^{25} - 34q^{27} - 56q^{28} + 78q^{30} - 32q^{31} - 10q^{33} - 52q^{34} - 26q^{36} - 56q^{37} + 70q^{39} - 36q^{40} - 10q^{42} - 52q^{43} - 140q^{45} - 180q^{46} - 2q^{48} - 52q^{49} - 26q^{51} - 64q^{52} - 22q^{54} + 132q^{55} - 22q^{57} - 60q^{58} - 18q^{60} - 92q^{61} + 108q^{63} - 52q^{64} - 124q^{66} - 240q^{67} - 104q^{69} - 268q^{70} - 2q^{72} - 56q^{73} + 104q^{75} - 48q^{76} - 22q^{78} - 12q^{79} + 2q^{81} + 208q^{82} - 22q^{84} - 52q^{85} - 26q^{87} - 260q^{88} - 26q^{90} - 32q^{91} - 176q^{93} - 240q^{94} + 292q^{96} - 80q^{97} - 58q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(507, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
507.2.s.a \(1392\) \(4.048\) None \(0\) \(-22\) \(0\) \(-56\)