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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
207.2.m.a \(440\) \(1.653\) None \(-9\) \(-20\) \(-11\) \(-9\)