Properties

Label 507.2.m
Level $507$
Weight $2$
Character orbit 507.m
Rep. character $\chi_{507}(40,\cdot)$
Character field $\Q(\zeta_{13})$
Dimension $384$
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.m (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{13})\)
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 744 384 360
Cusp forms 696 384 312
Eisenstein series 48 0 48

Trace form

\( 384q - 2q^{2} - 2q^{3} - 36q^{4} - 8q^{5} - 4q^{7} - 6q^{8} - 32q^{9} + O(q^{10}) \) \( 384q - 2q^{2} - 2q^{3} - 36q^{4} - 8q^{5} - 4q^{7} - 6q^{8} - 32q^{9} - 8q^{10} - 12q^{11} - 6q^{12} + 40q^{13} - 24q^{14} - 4q^{15} - 60q^{16} - 20q^{17} - 2q^{18} - 20q^{19} - 56q^{20} - 12q^{21} + 16q^{22} - 12q^{23} - 12q^{24} - 60q^{25} - 42q^{26} - 2q^{27} - 44q^{28} - 16q^{29} - 4q^{30} + 24q^{31} + 56q^{32} - 4q^{33} + 62q^{34} - 20q^{35} - 36q^{36} - 32q^{37} + 82q^{38} - 10q^{39} + 14q^{40} - 64q^{41} + 94q^{42} - 28q^{43} - 76q^{44} - 8q^{45} - 80q^{46} - 36q^{47} - 30q^{48} + 68q^{49} - 86q^{50} - 16q^{51} + 42q^{52} + 116q^{53} + 62q^{55} - 128q^{56} - 20q^{57} - 24q^{58} + 132q^{59} + 44q^{60} - 48q^{61} + 30q^{62} - 4q^{63} - 128q^{64} - 80q^{65} + 72q^{66} + 88q^{67} + 58q^{68} - 12q^{69} + 56q^{70} + 2q^{71} - 6q^{72} - 88q^{73} + 94q^{74} - 30q^{75} + 104q^{76} - 64q^{77} + 90q^{78} - 76q^{79} - 184q^{80} - 32q^{81} + 42q^{82} - 84q^{83} - 36q^{84} + 76q^{85} + 60q^{86} + 64q^{87} + 104q^{88} - 112q^{89} - 8q^{90} + 4q^{91} - 132q^{92} + 110q^{93} + 2q^{94} - 12q^{95} - 64q^{96} + 52q^{97} - 178q^{98} - 12q^{99} + O(q^{100}) \)

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.m.a \(180\) \(4.048\) None \(-1\) \(15\) \(-2\) \(4\)
507.2.m.b \(204\) \(4.048\) None \(-1\) \(-17\) \(-6\) \(-8\)

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

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