Properties

Label 403.2.bi
Level 403
Weight 2
Character orbit bi
Rep. character \(\chi_{403}(14,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 256
Newforms 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.bi (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 31 \)
Character field: \(\Q(\zeta_{15})\)
Newforms: \( 2 \)
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 320 256 64
Cusp forms 288 256 32
Eisenstein series 32 0 32

Trace form

\( 256q + 4q^{3} - 56q^{4} - 2q^{5} - 20q^{6} - 24q^{7} - 12q^{8} + 36q^{9} + O(q^{10}) \) \( 256q + 4q^{3} - 56q^{4} - 2q^{5} - 20q^{6} - 24q^{7} - 12q^{8} + 36q^{9} + 10q^{10} + 8q^{11} + 16q^{12} + 2q^{13} - 6q^{14} - 22q^{15} - 80q^{16} - 6q^{17} - 48q^{19} - 2q^{20} + 2q^{21} + 26q^{22} + 10q^{23} + 92q^{24} - 114q^{25} - 24q^{26} - 32q^{27} - 6q^{28} + 32q^{29} + 32q^{30} + 136q^{32} + 22q^{33} + 36q^{34} + 20q^{35} - 148q^{36} + 20q^{37} - 18q^{38} + 66q^{40} - 22q^{41} - 122q^{42} - 14q^{43} - 18q^{44} - 128q^{45} - 56q^{46} - 72q^{47} - 82q^{48} - 34q^{49} - 42q^{50} + 10q^{51} + 6q^{52} - 44q^{53} + 108q^{54} + 46q^{55} - 12q^{56} - 48q^{57} + 112q^{58} - 18q^{59} + 200q^{60} - 20q^{61} + 32q^{62} + 24q^{63} - 136q^{64} + 2q^{65} + 100q^{66} - 38q^{67} + 68q^{68} - 62q^{69} - 94q^{70} + 30q^{71} - 12q^{72} - 116q^{74} + 60q^{75} - 28q^{76} + 76q^{77} + 14q^{79} + 72q^{80} + 90q^{81} - 22q^{82} - 30q^{83} - 250q^{84} - 56q^{85} - 66q^{86} + 40q^{87} + 98q^{88} - 62q^{89} + 158q^{90} - 16q^{91} + 32q^{92} + 44q^{93} - 76q^{94} + 90q^{95} - 52q^{96} + 22q^{97} + 78q^{98} - 60q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(403, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
403.2.bi.a \(120\) \(3.218\) None \(6\) \(2\) \(13\) \(-16\)
403.2.bi.b \(136\) \(3.218\) None \(-6\) \(2\) \(-15\) \(-8\)

Decomposition of \(S_{2}^{\mathrm{old}}(403, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(403, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 2}\)