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Properties

Label 403.2.bl
Level 403
Weight 2
Character orbit bl
Rep. character \(\chi_{403}(16,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 288
Newform subspaces 2
Sturm bound 74
Trace bound 1

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Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.bl (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 2 \)
Sturm bound: \(74\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(403, [\chi])\).

Total New Old
Modular forms 320 320 0
Cusp forms 288 288 0
Eisenstein series 32 32 0

Trace form

\( 288q - 3q^{2} - 5q^{3} + 33q^{4} - 32q^{5} - 10q^{6} - 5q^{7} - 2q^{8} + 31q^{9} + O(q^{10}) \) \( 288q - 3q^{2} - 5q^{3} + 33q^{4} - 32q^{5} - 10q^{6} - 5q^{7} - 2q^{8} + 31q^{9} - 9q^{10} - 6q^{11} + 14q^{12} - 5q^{13} - 48q^{14} - 12q^{15} + 45q^{16} - 3q^{17} + 6q^{18} - q^{19} + 15q^{20} + 38q^{21} - 34q^{22} - 18q^{23} + 43q^{24} + 232q^{25} - 6q^{26} - 68q^{27} + 3q^{28} - 23q^{29} - 36q^{30} - 60q^{31} - 26q^{32} - 25q^{33} - 136q^{34} - 28q^{35} - 152q^{36} - 26q^{37} + 16q^{38} + 18q^{39} - 116q^{40} + 13q^{41} + 31q^{42} - 28q^{43} + 12q^{44} - 52q^{45} - 15q^{46} - 20q^{47} - 11q^{48} + 45q^{49} - 21q^{50} - 104q^{51} + 62q^{52} + 16q^{53} + 49q^{54} - 40q^{55} - 78q^{56} + 140q^{57} + 31q^{58} - 19q^{59} - 52q^{60} + 34q^{61} + 3q^{62} - 122q^{63} - 102q^{64} + 17q^{65} + 16q^{66} + 6q^{67} + 86q^{68} - 67q^{69} - 22q^{70} + 41q^{71} + 47q^{72} - 56q^{73} - 9q^{74} - 4q^{75} - 34q^{76} + 40q^{77} - 72q^{78} + 80q^{79} - 114q^{80} - 29q^{81} + 45q^{82} - 134q^{83} + 81q^{84} - 54q^{85} + 212q^{86} - 38q^{87} + 82q^{88} + 21q^{89} - 26q^{90} + 46q^{91} - 336q^{92} - 30q^{93} - 18q^{94} + 34q^{95} + 186q^{96} + 13q^{97} + 88q^{98} - 60q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(403, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
403.2.bl.a \(8\) \(3.218\) \(\Q(\zeta_{15})\) None \(-4\) \(-5\) \(-24\) \(-3\) \(q+(-2+\zeta_{15}+\zeta_{15}^{2}-2\zeta_{15}^{3}+2\zeta_{15}^{4}+\cdots)q^{2}+\cdots\)
403.2.bl.b \(280\) \(3.218\) None \(1\) \(0\) \(-8\) \(-2\)