Properties

Label 507.2.q
Level $507$
Weight $2$
Character orbit 507.q
Rep. character $\chi_{507}(16,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $744$
Newform subspaces $2$
Sturm bound $121$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.q (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{39})\)
Newform subspaces: \( 2 \)
Sturm bound: \(121\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 1512 744 768
Cusp forms 1416 744 672
Eisenstein series 96 0 96

Trace form

\( 744q + 2q^{2} + q^{3} + 32q^{4} + 8q^{5} - q^{7} - 12q^{8} + 31q^{9} + O(q^{10}) \) \( 744q + 2q^{2} + q^{3} + 32q^{4} + 8q^{5} - q^{7} - 12q^{8} + 31q^{9} + 2q^{10} - 6q^{11} - 4q^{12} - 34q^{13} + 24q^{14} - 2q^{15} + 26q^{16} - 10q^{17} - 4q^{18} + 2q^{20} + 10q^{21} - 64q^{22} - 6q^{23} + 12q^{24} - 46q^{25} - 30q^{26} - 2q^{27} - 18q^{28} - 8q^{29} + 4q^{30} - 62q^{31} - 116q^{32} - 2q^{33} - 134q^{34} - 10q^{35} + 32q^{36} + 12q^{37} - 82q^{38} + 6q^{39} - 50q^{40} + 10q^{41} + 248q^{42} - q^{43} + 16q^{44} - 4q^{45} - 4q^{46} - 12q^{47} - 4q^{48} - 140q^{49} - 28q^{50} - 8q^{51} - 100q^{52} - 128q^{53} - 134q^{55} - 40q^{56} - 24q^{57} - 78q^{58} + 402q^{59} - 104q^{60} + q^{61} - 150q^{62} - q^{63} - 44q^{64} - 4q^{65} - 96q^{66} - 153q^{67} - 136q^{68} + 6q^{69} - 200q^{70} + 190q^{71} + 6q^{72} + 2q^{73} - 196q^{74} - q^{75} + 56q^{76} + 28q^{77} - 102q^{78} + 2q^{79} + 22q^{80} + 31q^{81} - 132q^{82} + 48q^{83} - 14q^{84} - 142q^{85} - 156q^{86} - 106q^{87} + 484q^{88} + 4q^{89} - 4q^{90} - 135q^{91} + 24q^{92} - 3q^{93} - 170q^{94} + 168q^{95} - 8q^{96} - 171q^{97} + 22q^{98} + 12q^{99} + O(q^{100}) \)

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.q.a \(360\) \(4.048\) None \(1\) \(-15\) \(2\) \(2\)
507.2.q.b \(384\) \(4.048\) None \(1\) \(16\) \(6\) \(-3\)

Decomposition of \(S_{2}^{\mathrm{old}}(507, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(507, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)