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

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

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.t.a 507.t 169.k $336$ $4.048$ None 507.2.t.a \(0\) \(14\) \(0\) \(0\) $\mathrm{SU}(2)[C_{78}]$
507.2.t.b 507.t 169.k $360$ $4.048$ None 507.2.t.b \(0\) \(-15\) \(0\) \(3\) $\mathrm{SU}(2)[C_{78}]$

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

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