↑

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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
507.2.s.a 507.s 507.s $1392$ $4.048$ None 507.2.s.a \(0\) \(-22\) \(0\) \(-56\) $\mathrm{SU}(2)[C_{52}]$