Properties

Label 403.2.c
Level 403
Weight 2
Character orbit c
Rep. character \(\chi_{403}(311,\cdot)\)
Character field \(\Q\)
Dimension 34
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q\)
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 38 34 4
Cusp forms 34 34 0
Eisenstein series 4 0 4

Trace form

\( 34q - 32q^{4} + 22q^{9} + O(q^{10}) \) \( 34q - 32q^{4} + 22q^{9} + 4q^{10} - 8q^{12} + 6q^{13} - 16q^{14} + 36q^{16} - 12q^{17} - 16q^{22} - 16q^{23} - 18q^{25} + 18q^{26} + 12q^{27} + 40q^{30} + 12q^{35} - 40q^{36} + 12q^{38} - 4q^{39} + 28q^{40} + 28q^{42} - 24q^{43} + 16q^{48} - 58q^{49} - 8q^{51} - 72q^{52} - 20q^{53} + 36q^{55} + 8q^{56} + 36q^{61} + 8q^{62} - 60q^{64} - 42q^{65} - 68q^{66} + 56q^{68} + 4q^{69} + 16q^{74} - 44q^{75} - 28q^{77} - 20q^{78} + 32q^{79} - 38q^{81} + 12q^{82} - 40q^{87} + 80q^{88} + 68q^{90} + 10q^{91} + 12q^{92} + 88q^{94} + 20q^{95} + O(q^{100}) \)

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.c.a \(2\) \(3.218\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) \(q+2q^{3}+2q^{4}+4iq^{5}-2iq^{7}+q^{9}+\cdots\)
403.2.c.b \(32\) \(3.218\) None \(0\) \(-4\) \(0\) \(0\)