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Properties

Label 207.2.m
Level $207$
Weight $2$
Character orbit 207.m
Rep. character $\chi_{207}(4,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $440$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 207.m (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{33})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(207, [\chi])\).

Total New Old
Modular forms 520 520 0
Cusp forms 440 440 0
Eisenstein series 80 80 0

Trace form

\( 440 q - 9 q^{2} - 20 q^{3} + 11 q^{4} - 11 q^{5} - 17 q^{6} - 9 q^{7} - 50 q^{8} - 24 q^{9} + O(q^{10}) \) \( 440 q - 9 q^{2} - 20 q^{3} + 11 q^{4} - 11 q^{5} - 17 q^{6} - 9 q^{7} - 50 q^{8} - 24 q^{9} - 44 q^{10} - 17 q^{11} - 30 q^{12} - 9 q^{13} - 21 q^{14} - 34 q^{15} + 11 q^{16} - 20 q^{17} + 3 q^{18} - 36 q^{19} - 25 q^{20} + 3 q^{21} - 28 q^{22} - 5 q^{23} - 172 q^{24} + 11 q^{25} - 48 q^{26} + 31 q^{27} - 60 q^{28} + 9 q^{29} + 12 q^{30} - 3 q^{31} - 3 q^{32} - 44 q^{33} - 17 q^{34} - 56 q^{35} + 47 q^{36} - 48 q^{37} + 3 q^{38} - 64 q^{39} + 55 q^{40} - 9 q^{41} - 80 q^{42} - 9 q^{43} + 24 q^{44} - 56 q^{45} - 44 q^{46} - 12 q^{47} + 4 q^{48} - 53 q^{49} + 27 q^{50} + 14 q^{51} - 12 q^{52} - 84 q^{53} - 18 q^{54} - 68 q^{55} - 125 q^{56} + 27 q^{57} - 8 q^{58} + 81 q^{59} + 88 q^{60} + 3 q^{61} + 58 q^{62} + 43 q^{63} - 70 q^{64} - 84 q^{65} + 35 q^{66} - 3 q^{67} + 194 q^{68} + 33 q^{69} - 10 q^{70} + 86 q^{71} + 182 q^{72} - 36 q^{73} - 57 q^{74} + 55 q^{75} - 21 q^{76} + 91 q^{77} + 191 q^{78} - 9 q^{79} + 220 q^{80} - 228 q^{81} - 62 q^{82} - 68 q^{83} + 144 q^{84} + q^{85} - 53 q^{86} + 160 q^{87} + 83 q^{88} - 28 q^{89} - 314 q^{90} - 108 q^{91} + q^{92} + 132 q^{93} + 48 q^{94} - 3 q^{95} + 174 q^{96} - 36 q^{97} - 156 q^{98} - 220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(207, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
207.2.m.a 207.m 207.m $440$ $1.653$ None \(-9\) \(-20\) \(-11\) \(-9\) $\mathrm{SU}(2)[C_{33}]$