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Properties

Label 507.2.m
Level $507$
Weight $2$
Character orbit 507.m
Rep. character $\chi_{507}(40,\cdot)$
Character field $\Q(\zeta_{13})$
Dimension $384$
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.m (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{13})\)
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 744 384 360
Cusp forms 696 384 312
Eisenstein series 48 0 48

Trace form

\( 384 q - 2 q^{2} - 2 q^{3} - 36 q^{4} - 8 q^{5} - 4 q^{7} - 6 q^{8} - 32 q^{9} + O(q^{10}) \) \( 384 q - 2 q^{2} - 2 q^{3} - 36 q^{4} - 8 q^{5} - 4 q^{7} - 6 q^{8} - 32 q^{9} - 8 q^{10} - 12 q^{11} - 6 q^{12} + 40 q^{13} - 24 q^{14} - 4 q^{15} - 60 q^{16} - 20 q^{17} - 2 q^{18} - 20 q^{19} - 56 q^{20} - 12 q^{21} + 16 q^{22} - 12 q^{23} - 12 q^{24} - 60 q^{25} - 42 q^{26} - 2 q^{27} - 44 q^{28} - 16 q^{29} - 4 q^{30} + 24 q^{31} + 56 q^{32} - 4 q^{33} + 62 q^{34} - 20 q^{35} - 36 q^{36} - 32 q^{37} + 82 q^{38} - 10 q^{39} + 14 q^{40} - 64 q^{41} + 94 q^{42} - 28 q^{43} - 76 q^{44} - 8 q^{45} - 80 q^{46} - 36 q^{47} - 30 q^{48} + 68 q^{49} - 86 q^{50} - 16 q^{51} + 42 q^{52} + 116 q^{53} + 62 q^{55} - 128 q^{56} - 20 q^{57} - 24 q^{58} + 132 q^{59} + 44 q^{60} - 48 q^{61} + 30 q^{62} - 4 q^{63} - 128 q^{64} - 80 q^{65} + 72 q^{66} + 88 q^{67} + 58 q^{68} - 12 q^{69} + 56 q^{70} + 2 q^{71} - 6 q^{72} - 88 q^{73} + 94 q^{74} - 30 q^{75} + 104 q^{76} - 64 q^{77} + 90 q^{78} - 76 q^{79} - 184 q^{80} - 32 q^{81} + 42 q^{82} - 84 q^{83} - 36 q^{84} + 76 q^{85} + 60 q^{86} + 64 q^{87} + 104 q^{88} - 112 q^{89} - 8 q^{90} + 4 q^{91} - 132 q^{92} + 110 q^{93} + 2 q^{94} - 12 q^{95} - 64 q^{96} + 52 q^{97} - 178 q^{98} - 12 q^{99} + O(q^{100}) \)

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.m.a 507.m 169.g $180$ $4.048$ None 507.2.m.a \(-1\) \(15\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{13}]$
507.2.m.b 507.m 169.g $204$ $4.048$ None 507.2.m.b \(-1\) \(-17\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{13}]$

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

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