Properties

Label 56.2.b
Level $56$
Weight $2$
Character orbit 56.b
Rep. character $\chi_{56}(29,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 56 = 2^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 56.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(56, [\chi])\).

Total New Old
Modular forms 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

Trace form

\( 6q - q^{2} - 3q^{4} + 2q^{6} - 2q^{7} - 7q^{8} - 6q^{9} + O(q^{10}) \) \( 6q - q^{2} - 3q^{4} + 2q^{6} - 2q^{7} - 7q^{8} - 6q^{9} - 4q^{10} + 14q^{12} + q^{14} + 8q^{15} + q^{16} - 4q^{17} - 15q^{18} + 4q^{20} - 6q^{22} - 8q^{23} + 6q^{24} - 2q^{25} + 20q^{26} - 5q^{28} + 16q^{30} - 16q^{31} + 9q^{32} + 8q^{33} - 2q^{34} + 11q^{36} + 18q^{38} + 8q^{39} - 28q^{40} - 4q^{41} - 10q^{42} - 18q^{44} + 16q^{46} - 10q^{48} + 6q^{49} + 19q^{50} - 4q^{52} - 44q^{54} + 32q^{55} + 7q^{56} - 8q^{57} - 20q^{58} - 24q^{60} - 32q^{62} + 10q^{63} - 15q^{64} + 16q^{65} - 4q^{66} + 26q^{68} + 12q^{70} - 32q^{71} + 31q^{72} - 20q^{73} - 12q^{74} + 14q^{76} - 16q^{78} + 16q^{79} + 36q^{80} + 14q^{81} + 38q^{82} - 14q^{84} + 26q^{86} + 32q^{87} + 38q^{88} - 20q^{89} + 20q^{90} + 8q^{92} - 8q^{95} - 58q^{96} - 4q^{97} - q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(56, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
56.2.b.a \(2\) \(0.447\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{2}+\beta q^{3}-2q^{4}-\beta q^{5}-2q^{6}+\cdots\)
56.2.b.b \(4\) \(0.447\) 4.0.2312.1 None \(-1\) \(0\) \(0\) \(-4\) \(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)