Properties

Label 77.2.i
Level $77$
Weight $2$
Character orbit 77.i
Rep. character $\chi_{77}(10,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 77 = 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 77.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
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 \(M_{2}(77, [\chi])\).

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

Trace form

\( 12q - 6q^{3} + 4q^{4} - 4q^{9} + O(q^{10}) \) \( 12q - 6q^{3} + 4q^{4} - 4q^{9} - 4q^{11} - 18q^{12} + 8q^{14} - 20q^{15} + 12q^{16} - 4q^{22} - 20q^{23} + 14q^{25} + 18q^{26} + 6q^{31} + 18q^{33} - 12q^{36} + 16q^{37} - 48q^{38} + 16q^{42} + 20q^{44} + 54q^{45} - 18q^{47} + 16q^{49} - 2q^{53} + 18q^{56} - 6q^{58} - 12q^{59} + 28q^{64} - 42q^{66} - 24q^{67} - 58q^{70} + 20q^{71} - 78q^{75} - 50q^{77} + 8q^{78} + 30q^{80} + 14q^{81} + 54q^{82} - 38q^{86} - 4q^{88} - 66q^{89} + 22q^{91} - 20q^{92} + 12q^{93} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(77, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
77.2.i.a \(12\) \(0.615\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-6\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{7})q^{2}+(-1+\beta _{2}-\beta _{8}-\beta _{9}+\cdots)q^{3}+\cdots\)