Properties

Label 13.4.b
Level 13
Weight 4
Character orbit b
Rep. character \(\chi_{13}(12,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 13.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(13, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

Trace form

\(2q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut 54q^{10} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 52q^{13} \) \(\mathstrut +\mathstrut 90q^{14} \) \(\mathstrut -\mathstrut 142q^{16} \) \(\mathstrut -\mathstrut 90q^{17} \) \(\mathstrut -\mathstrut 288q^{22} \) \(\mathstrut +\mathstrut 324q^{23} \) \(\mathstrut +\mathstrut 88q^{25} \) \(\mathstrut +\mathstrut 234q^{26} \) \(\mathstrut +\mathstrut 106q^{27} \) \(\mathstrut -\mathstrut 288q^{29} \) \(\mathstrut -\mathstrut 54q^{30} \) \(\mathstrut -\mathstrut 270q^{35} \) \(\mathstrut +\mathstrut 52q^{36} \) \(\mathstrut -\mathstrut 36q^{38} \) \(\mathstrut -\mathstrut 52q^{39} \) \(\mathstrut +\mathstrut 378q^{40} \) \(\mathstrut -\mathstrut 90q^{42} \) \(\mathstrut -\mathstrut 194q^{43} \) \(\mathstrut +\mathstrut 142q^{48} \) \(\mathstrut +\mathstrut 236q^{49} \) \(\mathstrut +\mathstrut 90q^{51} \) \(\mathstrut -\mathstrut 52q^{52} \) \(\mathstrut -\mathstrut 828q^{53} \) \(\mathstrut +\mathstrut 864q^{55} \) \(\mathstrut +\mathstrut 630q^{56} \) \(\mathstrut +\mathstrut 752q^{61} \) \(\mathstrut -\mathstrut 1584q^{62} \) \(\mathstrut -\mathstrut 866q^{64} \) \(\mathstrut -\mathstrut 702q^{65} \) \(\mathstrut +\mathstrut 288q^{66} \) \(\mathstrut +\mathstrut 90q^{68} \) \(\mathstrut -\mathstrut 324q^{69} \) \(\mathstrut +\mathstrut 1818q^{74} \) \(\mathstrut -\mathstrut 88q^{75} \) \(\mathstrut +\mathstrut 1440q^{77} \) \(\mathstrut -\mathstrut 234q^{78} \) \(\mathstrut -\mathstrut 1660q^{79} \) \(\mathstrut +\mathstrut 1298q^{81} \) \(\mathstrut +\mathstrut 1152q^{82} \) \(\mathstrut +\mathstrut 288q^{87} \) \(\mathstrut -\mathstrut 2016q^{88} \) \(\mathstrut -\mathstrut 1404q^{90} \) \(\mathstrut -\mathstrut 1170q^{91} \) \(\mathstrut -\mathstrut 324q^{92} \) \(\mathstrut +\mathstrut 666q^{94} \) \(\mathstrut +\mathstrut 108q^{95} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(13, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
13.4.b.a \(2\) \(0.767\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)