Properties

Label 8.3.d
Level 8
Weight 3
Character orbit d
Rep. character \(\chi_{8}(3,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 8.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(8, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\(q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut -\mathstrut 28q^{22} \) \(\mathstrut +\mathstrut 16q^{24} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut +\mathstrut 28q^{27} \) \(\mathstrut -\mathstrut 32q^{32} \) \(\mathstrut -\mathstrut 28q^{33} \) \(\mathstrut -\mathstrut 4q^{34} \) \(\mathstrut -\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 68q^{38} \) \(\mathstrut -\mathstrut 46q^{41} \) \(\mathstrut +\mathstrut 14q^{43} \) \(\mathstrut +\mathstrut 56q^{44} \) \(\mathstrut -\mathstrut 32q^{48} \) \(\mathstrut +\mathstrut 49q^{49} \) \(\mathstrut -\mathstrut 50q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 56q^{54} \) \(\mathstrut +\mathstrut 68q^{57} \) \(\mathstrut -\mathstrut 82q^{59} \) \(\mathstrut +\mathstrut 64q^{64} \) \(\mathstrut +\mathstrut 56q^{66} \) \(\mathstrut +\mathstrut 62q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 142q^{73} \) \(\mathstrut -\mathstrut 50q^{75} \) \(\mathstrut -\mathstrut 136q^{76} \) \(\mathstrut -\mathstrut 11q^{81} \) \(\mathstrut +\mathstrut 92q^{82} \) \(\mathstrut +\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 28q^{86} \) \(\mathstrut -\mathstrut 112q^{88} \) \(\mathstrut +\mathstrut 146q^{89} \) \(\mathstrut +\mathstrut 64q^{96} \) \(\mathstrut -\mathstrut 94q^{97} \) \(\mathstrut -\mathstrut 98q^{98} \) \(\mathstrut -\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(8, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
8.3.d.a \(1\) \(0.218\) \(\Q\) \(\Q(\sqrt{-2}) \) \(-2\) \(-2\) \(0\) \(0\) \(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots\)