Properties

Label 207.2.o
Level $207$
Weight $2$
Character orbit 207.o
Rep. character $\chi_{207}(5,\cdot)$
Character field $\Q(\zeta_{66})$
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.o (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{66})\)
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

\( 440q - 27q^{2} - 16q^{3} - 29q^{4} - 33q^{5} - 25q^{6} - 11q^{7} - 16q^{9} + O(q^{10}) \) \( 440q - 27q^{2} - 16q^{3} - 29q^{4} - 33q^{5} - 25q^{6} - 11q^{7} - 16q^{9} - 44q^{10} - 33q^{11} - 22q^{12} - 9q^{13} - 33q^{14} + 3q^{16} - 39q^{18} - 44q^{19} - 33q^{20} - 55q^{21} - 27q^{23} + 52q^{24} + 11q^{25} - 79q^{27} - 44q^{28} + 27q^{29} - 66q^{30} - 3q^{31} - 33q^{32} - 11q^{34} + 23q^{36} - 44q^{37} - 33q^{38} - 40q^{39} - 77q^{40} + 9q^{41} - 22q^{42} - 11q^{43} - 36q^{46} - 120q^{47} - 56q^{48} + 35q^{49} - 3q^{50} - 22q^{51} - 38q^{52} + 42q^{54} - 44q^{55} + 165q^{56} + 11q^{57} - 10q^{58} - 9q^{59} + 88q^{60} - 11q^{61} + 33q^{63} - 22q^{64} + 198q^{65} + 33q^{66} - 11q^{67} + 3q^{69} - 70q^{70} + 14q^{72} - 36q^{73} + 231q^{74} - 13q^{75} - 11q^{76} + 39q^{77} + 3q^{78} - 11q^{79} + 172q^{81} - 10q^{82} + 66q^{83} - 110q^{84} + q^{85} - 33q^{86} - 196q^{87} - 99q^{88} + 418q^{90} + 63q^{92} - 188q^{93} - 42q^{94} - 93q^{95} - 82q^{96} + 22q^{97} + 242q^{99} + O(q^{100}) \)

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.o.a \(440\) \(1.653\) None \(-27\) \(-16\) \(-33\) \(-11\)