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Properties

Label 507.2.q
Level $507$
Weight $2$
Character orbit 507.q
Rep. character $\chi_{507}(16,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $744$
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.q (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{39})\)
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 744 768
Cusp forms 1416 744 672
Eisenstein series 96 0 96

Trace form

\( 744 q + 2 q^{2} + q^{3} + 32 q^{4} + 8 q^{5} - q^{7} - 12 q^{8} + 31 q^{9} + O(q^{10}) \) \( 744 q + 2 q^{2} + q^{3} + 32 q^{4} + 8 q^{5} - q^{7} - 12 q^{8} + 31 q^{9} + 2 q^{10} - 6 q^{11} - 4 q^{12} - 34 q^{13} + 24 q^{14} - 2 q^{15} + 26 q^{16} - 10 q^{17} - 4 q^{18} + 2 q^{20} + 10 q^{21} - 64 q^{22} - 6 q^{23} + 12 q^{24} - 46 q^{25} - 30 q^{26} - 2 q^{27} - 18 q^{28} - 8 q^{29} + 4 q^{30} - 62 q^{31} - 116 q^{32} - 2 q^{33} - 134 q^{34} - 10 q^{35} + 32 q^{36} + 12 q^{37} - 82 q^{38} + 6 q^{39} - 50 q^{40} + 10 q^{41} + 248 q^{42} - q^{43} + 16 q^{44} - 4 q^{45} - 4 q^{46} - 12 q^{47} - 4 q^{48} - 140 q^{49} - 28 q^{50} - 8 q^{51} - 100 q^{52} - 128 q^{53} - 134 q^{55} - 40 q^{56} - 24 q^{57} - 78 q^{58} + 402 q^{59} - 104 q^{60} + q^{61} - 150 q^{62} - q^{63} - 44 q^{64} - 4 q^{65} - 96 q^{66} - 153 q^{67} - 136 q^{68} + 6 q^{69} - 200 q^{70} + 190 q^{71} + 6 q^{72} + 2 q^{73} - 196 q^{74} - q^{75} + 56 q^{76} + 28 q^{77} - 102 q^{78} + 2 q^{79} + 22 q^{80} + 31 q^{81} - 132 q^{82} + 48 q^{83} - 14 q^{84} - 142 q^{85} - 156 q^{86} - 106 q^{87} + 484 q^{88} + 4 q^{89} - 4 q^{90} - 135 q^{91} + 24 q^{92} - 3 q^{93} - 170 q^{94} + 168 q^{95} - 8 q^{96} - 171 q^{97} + 22 q^{98} + 12 q^{99} + O(q^{100}) \)

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.q.a 507.q 169.i $360$ $4.048$ None 507.2.q.a \(1\) \(-15\) \(2\) \(2\) $\mathrm{SU}(2)[C_{39}]$
507.2.q.b 507.q 169.i $384$ $4.048$ None 507.2.q.b \(1\) \(16\) \(6\) \(-3\) $\mathrm{SU}(2)[C_{39}]$

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

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