Properties

Label 507.2.x
Level $507$
Weight $2$
Character orbit 507.x
Rep. character $\chi_{507}(2,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $2832$
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.x (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 507 \)
Character field: \(\Q(\zeta_{156})\)
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 3024 3024 0
Cusp forms 2832 2832 0
Eisenstein series 192 192 0

Trace form

\( 2832 q - 50 q^{3} - 92 q^{4} - 50 q^{6} - 90 q^{7} - 50 q^{9} + O(q^{10}) \) \( 2832 q - 50 q^{3} - 92 q^{4} - 50 q^{6} - 90 q^{7} - 50 q^{9} - 116 q^{10} - 52 q^{12} - 112 q^{13} - 38 q^{15} - 212 q^{16} - 56 q^{18} - 102 q^{19} - 74 q^{21} - 48 q^{22} + 86 q^{24} - 104 q^{25} - 32 q^{27} - 104 q^{28} - 174 q^{30} - 98 q^{31} - 68 q^{33} - 68 q^{34} - 16 q^{36} - 74 q^{37} - 118 q^{39} - 96 q^{40} - 44 q^{42} - 134 q^{43} + 98 q^{45} - 58 q^{48} - 122 q^{49} - 52 q^{51} - 180 q^{52} - 98 q^{54} - 324 q^{55} - 80 q^{57} - 132 q^{58} - 96 q^{60} - 124 q^{61} - 198 q^{63} - 104 q^{64} + 58 q^{66} + 112 q^{67} + 26 q^{69} + 136 q^{70} - 64 q^{72} - 42 q^{73} - 164 q^{75} - 68 q^{76} + 28 q^{78} - 120 q^{79} - 38 q^{81} - 340 q^{82} - 44 q^{84} - 116 q^{85} - 34 q^{87} + 116 q^{88} - 52 q^{90} - 114 q^{91} + 68 q^{93} + 36 q^{94} - 406 q^{96} - 86 q^{97} - 92 q^{99} + O(q^{100}) \)

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.x.a 507.x 507.x $48$ $4.048$ \(\Q(\sqrt{-3}) \) 507.2.x.a \(0\) \(0\) \(0\) \(10\) $\mathrm{U}(1)[D_{156}]$
507.2.x.b 507.x 507.x $2784$ $4.048$ None 507.2.x.b \(0\) \(-50\) \(0\) \(-100\) $\mathrm{SU}(2)[C_{156}]$