Properties

Label 507.2.p
Level $507$
Weight $2$
Character orbit 507.p
Rep. character $\chi_{507}(25,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $360$
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.p (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{26})\)
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 744 360 384
Cusp forms 696 360 336
Eisenstein series 48 0 48

Trace form

\( 360q + 2q^{3} + 30q^{4} - 30q^{9} + O(q^{10}) \) \( 360q + 2q^{3} + 30q^{4} - 30q^{9} - 4q^{10} - 6q^{12} - 50q^{13} - 8q^{14} - 14q^{16} + 8q^{17} - 56q^{22} - 4q^{23} + 14q^{25} + 12q^{26} + 2q^{27} - 4q^{29} - 4q^{30} - 52q^{31} + 130q^{32} - 130q^{34} + 4q^{35} + 30q^{36} + 138q^{38} - 2q^{39} + 12q^{40} - 118q^{42} - 4q^{43} - 2q^{48} - 126q^{49} - 16q^{51} + 128q^{52} - 74q^{53} + 90q^{55} - 24q^{56} - 52q^{58} - 208q^{59} + 104q^{60} + 20q^{61} + 102q^{62} + 10q^{64} - 88q^{66} + 52q^{67} - 118q^{68} - 4q^{69} - 78q^{71} + 88q^{74} + 2q^{75} - 260q^{76} + 8q^{77} + 118q^{78} + 28q^{79} - 30q^{81} + 86q^{82} + 78q^{85} + 156q^{86} - 88q^{87} - 296q^{88} - 4q^{90} - 128q^{91} + 28q^{92} - 130q^{93} + 50q^{94} - 124q^{95} + 156q^{97} + O(q^{100}) \)

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.p.a \(168\) \(4.048\) None \(0\) \(-14\) \(0\) \(0\)
507.2.p.b \(192\) \(4.048\) None \(0\) \(16\) \(0\) \(0\)

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

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