Properties

Label 507.2.t
Level $507$
Weight $2$
Character orbit 507.t
Rep. character $\chi_{507}(4,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $696$
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.t (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{78})\)
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 696 816
Cusp forms 1416 696 720
Eisenstein series 96 0 96

Trace form

\( 696q - q^{3} - 26q^{4} + 3q^{7} + 29q^{9} + O(q^{10}) \) \( 696q - q^{3} - 26q^{4} + 3q^{7} + 29q^{9} + 4q^{10} + 6q^{11} - 4q^{12} + 32q^{13} + 8q^{14} - 6q^{15} + 28q^{16} + 4q^{17} - 6q^{19} - 12q^{20} + 44q^{22} - 2q^{23} + 62q^{25} + 2q^{27} - 6q^{28} - 2q^{29} + 4q^{30} + 52q^{31} - 130q^{32} + 6q^{33} + 130q^{34} + 2q^{35} - 26q^{36} - 138q^{38} - 2q^{39} + 24q^{40} + 12q^{41} - 260q^{42} + 11q^{43} - 6q^{45} - 12q^{48} + 140q^{49} - 8q^{51} - 120q^{52} + 86q^{53} - 102q^{55} + 12q^{56} + 52q^{58} - 410q^{59} - 104q^{60} - 15q^{61} - 114q^{62} - 3q^{63} - 6q^{65} + 112q^{66} - 67q^{67} + 106q^{68} + 10q^{69} - 138q^{71} - 64q^{74} + 15q^{75} - 40q^{76} - 44q^{77} - 130q^{78} + 46q^{79} + 24q^{80} + 29q^{81} - 110q^{82} - 6q^{84} - 78q^{85} - 156q^{86} + 94q^{87} - 496q^{88} - 12q^{89} - 8q^{90} + 113q^{91} + 80q^{92} - 3q^{93} - 38q^{94} - 200q^{95} - 147q^{97} + O(q^{100}) \)

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.t.a \(336\) \(4.048\) None \(0\) \(14\) \(0\) \(0\)
507.2.t.b \(360\) \(4.048\) None \(0\) \(-15\) \(0\) \(3\)

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

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