Properties

Label 49.2.g
Level $49$
Weight $2$
Character orbit 49.g
Rep. character $\chi_{49}(2,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $48$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 49.g (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(49, [\chi])\).

Total New Old
Modular forms 72 72 0
Cusp forms 48 48 0
Eisenstein series 24 24 0

Trace form

\( 48q - 13q^{2} - 14q^{3} - 9q^{4} - 14q^{5} - 14q^{7} - 20q^{8} + 6q^{9} + O(q^{10}) \) \( 48q - 13q^{2} - 14q^{3} - 9q^{4} - 14q^{5} - 14q^{7} - 20q^{8} + 6q^{9} - 14q^{10} - 3q^{11} + 21q^{12} - 14q^{13} + 21q^{14} - 12q^{15} - 3q^{16} - 7q^{17} + 2q^{18} + 21q^{19} + 14q^{20} - 14q^{21} - 20q^{22} + 15q^{23} + 28q^{24} - 4q^{25} + 7q^{27} + 28q^{28} + 12q^{29} + 11q^{30} + 35q^{31} + 45q^{32} - 14q^{33} + 70q^{34} - 12q^{36} + 15q^{37} - 28q^{38} - 7q^{39} - 42q^{40} - 42q^{41} + 28q^{42} - 30q^{43} - 50q^{44} + 7q^{45} - 78q^{46} + 21q^{47} - 84q^{48} - 70q^{49} + 40q^{50} - 52q^{51} - 70q^{52} + 11q^{53} - 77q^{54} - 7q^{55} - 28q^{56} - 12q^{57} + 16q^{58} - 28q^{59} + 56q^{60} + 7q^{61} - 28q^{62} + 35q^{63} - 32q^{64} + 14q^{65} + 154q^{66} + 11q^{67} + 77q^{68} + 70q^{69} + 70q^{70} + 19q^{71} + 170q^{72} + 7q^{73} + 34q^{74} + 112q^{75} + 119q^{76} + 7q^{77} + 28q^{78} + 15q^{79} + 70q^{80} + 64q^{81} - 14q^{82} - 84q^{84} - 26q^{85} - 33q^{86} - 112q^{87} - 77q^{88} - 14q^{89} - 182q^{90} + 84q^{91} - 38q^{92} - 80q^{93} + 14q^{94} - 61q^{95} - 70q^{96} - 161q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
49.2.g.a \(48\) \(0.391\) None \(-13\) \(-14\) \(-14\) \(-14\)