Properties

Label 48.2.k
Level 48
Weight 2
Character orbit k
Rep. character \(\chi_{48}(11,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 12
Newforms 1
Sturm bound 16
Trace bound 0

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Defining parameters

Level: \( N \) = \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 48.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 48 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(48, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

Trace form

\( 12q - 2q^{3} - 4q^{4} - 8q^{6} - 8q^{7} + O(q^{10}) \) \( 12q - 2q^{3} - 4q^{4} - 8q^{6} - 8q^{7} - 8q^{12} - 4q^{13} + 16q^{16} + 4q^{18} - 12q^{19} - 8q^{21} + 16q^{22} + 24q^{24} + 10q^{27} - 8q^{28} + 28q^{30} - 4q^{33} - 8q^{34} + 20q^{36} - 4q^{37} + 20q^{39} - 40q^{40} - 24q^{42} + 12q^{43} - 12q^{45} - 40q^{46} - 48q^{48} - 20q^{49} + 24q^{51} - 16q^{52} - 52q^{54} + 24q^{55} + 32q^{58} - 16q^{60} + 12q^{61} + 56q^{64} + 28q^{66} + 28q^{67} + 4q^{69} + 40q^{70} + 40q^{72} - 34q^{75} + 56q^{76} + 60q^{78} - 4q^{81} - 16q^{82} + 16q^{84} + 32q^{85} - 60q^{87} - 64q^{88} - 16q^{90} - 56q^{91} + 28q^{93} - 48q^{94} - 56q^{96} - 8q^{97} - 52q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(48, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
48.2.k.a \(12\) \(0.383\) 12.0.\(\cdots\).2 None \(0\) \(-2\) \(0\) \(-8\) \(q+\beta _{6}q^{2}-\beta _{10}q^{3}+(-\beta _{1}+\beta _{10}+\beta _{11})q^{4}+\cdots\)