Properties

Label 403.2.l
Level 403
Weight 2
Character orbit l
Rep. character \(\chi_{403}(25,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 72
Newforms 3
Sturm bound 74
Trace bound 5

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Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 3 \)
Sturm bound: \(74\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

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

Total New Old
Modular forms 80 80 0
Cusp forms 72 72 0
Eisenstein series 8 8 0

Trace form

\( 72q - 4q^{3} - 80q^{4} - 36q^{9} + O(q^{10}) \) \( 72q - 4q^{3} - 80q^{4} - 36q^{9} + 2q^{10} - 12q^{12} + 2q^{13} + 16q^{14} + 64q^{16} - 14q^{22} - 44q^{23} + 26q^{25} + 6q^{26} + 8q^{27} + 24q^{29} - 16q^{30} - 36q^{35} + 36q^{36} + 42q^{38} - 4q^{39} + 14q^{40} - 16q^{42} - 10q^{43} + 22q^{48} + 50q^{49} + 26q^{51} - 32q^{52} + 2q^{53} - 18q^{55} - 44q^{56} + 28q^{61} - 38q^{62} - 4q^{64} - 24q^{65} + 128q^{66} + 10q^{68} - 34q^{69} - 22q^{74} + 24q^{75} - 164q^{77} - 40q^{78} - 70q^{79} - 84q^{81} - 48q^{82} + 40q^{87} - 2q^{88} - 2q^{90} - 88q^{91} + 108q^{92} + 20q^{94} + 40q^{95} + O(q^{100}) \)

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.l.a \(2\) \(3.218\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(-3\) \(q+(1-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
403.2.l.b \(2\) \(3.218\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(3\) \(q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(1+\cdots)q^{5}+\cdots\)
403.2.l.c \(68\) \(3.218\) None \(0\) \(-6\) \(0\) \(0\)