Properties

Label 56.2.m
Level $56$
Weight $2$
Character orbit 56.m
Rep. character $\chi_{56}(3,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 56 = 2^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 56.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

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

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

Trace form

\( 12q - 6q^{3} - 12q^{8} + O(q^{10}) \) \( 12q - 6q^{3} - 12q^{8} + 6q^{10} - 6q^{11} - 18q^{12} + 6q^{14} - 6q^{17} + 6q^{18} - 6q^{19} + 24q^{22} + 6q^{24} + 6q^{26} + 6q^{28} - 12q^{30} - 6q^{33} + 18q^{35} + 48q^{36} - 24q^{38} + 42q^{40} - 30q^{42} + 6q^{44} - 18q^{46} - 12q^{49} - 48q^{50} + 6q^{51} - 24q^{52} - 36q^{54} - 36q^{57} + 18q^{58} + 42q^{59} - 6q^{60} - 72q^{64} - 12q^{65} + 12q^{66} + 30q^{67} - 36q^{68} + 30q^{70} + 18q^{73} + 12q^{74} + 24q^{75} + 60q^{78} + 36q^{80} + 6q^{81} + 54q^{82} + 12q^{84} + 6q^{88} + 18q^{89} - 72q^{91} + 60q^{92} - 12q^{94} + 60q^{96} - 6q^{98} - 24q^{99} + O(q^{100}) \)

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.m.a \(12\) \(0.447\) 12.0.\(\cdots\).2 None \(0\) \(-6\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{8})q^{2}+(-1-\beta _{10})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)