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Properties

Label 403.2.be
Level 403
Weight 2
Character orbit be
Rep. character \(\chi_{403}(57,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 144
Newforms 3
Sturm bound 74
Trace bound 6

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Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{12})\)
Newforms: \( 3 \)
Sturm bound: \(74\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

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

Total New Old
Modular forms 160 160 0
Cusp forms 144 144 0
Eisenstein series 16 16 0

Trace form

\( 144q - 8q^{2} - 12q^{3} - 2q^{5} - 36q^{6} - 4q^{7} - 4q^{8} + 64q^{9} + O(q^{10}) \) \( 144q - 8q^{2} - 12q^{3} - 2q^{5} - 36q^{6} - 4q^{7} - 4q^{8} + 64q^{9} - 12q^{11} - 6q^{13} + 24q^{14} - 160q^{16} - 40q^{18} - 4q^{19} + 22q^{20} - 42q^{21} + 60q^{22} + 48q^{24} - 18q^{26} + 2q^{28} + 26q^{31} - 16q^{32} - 12q^{33} + 24q^{34} - 8q^{35} + 6q^{37} - 40q^{39} + 12q^{40} - 2q^{41} - 48q^{42} - 72q^{44} + 10q^{50} + 120q^{52} + 24q^{53} - 12q^{55} - 84q^{57} + 14q^{59} + 48q^{63} + 66q^{65} - 176q^{66} + 10q^{67} - 168q^{70} - 38q^{71} + 74q^{72} + 12q^{73} + 72q^{74} + 64q^{76} + 84q^{78} + 96q^{79} + 50q^{80} - 32q^{81} - 18q^{83} - 114q^{84} - 102q^{86} + 64q^{87} - 140q^{93} - 32q^{94} + 192q^{96} + 12q^{97} + 20q^{98} - 24q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.be.a \(4\) \(3.218\) \(\Q(\zeta_{12})\) None \(-2\) \(6\) \(-2\) \(-10\) \(q+(-1+\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+\cdots\)
403.2.be.b \(4\) \(3.218\) \(\Q(\zeta_{12})\) None \(-2\) \(6\) \(-2\) \(8\) \(q+(-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
403.2.be.c \(136\) \(3.218\) None \(-4\) \(-24\) \(2\) \(-2\)