Properties

Label 77.2.b
Level $77$
Weight $2$
Character orbit 77.b
Rep. character $\chi_{77}(76,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 77 = 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 77.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(77, [\chi])\).

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

Trace form

\( 6q - 10q^{4} - 2q^{9} + O(q^{10}) \) \( 6q - 10q^{4} - 2q^{9} - 8q^{11} - 2q^{14} + 20q^{15} + 6q^{16} + 22q^{22} - 28q^{23} + 10q^{25} - 30q^{36} - 16q^{37} + 20q^{42} - 20q^{44} - 22q^{49} + 20q^{53} + 66q^{56} + 48q^{58} - 58q^{64} + 36q^{67} - 20q^{70} + 4q^{71} + 2q^{77} - 80q^{78} - 26q^{81} - 4q^{86} - 26q^{88} - 40q^{91} + 80q^{92} + 60q^{93} + 36q^{99} + O(q^{100}) \)

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.b.a \(2\) \(0.615\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-5q^{4}-\beta q^{7}+3\beta q^{8}+3q^{9}+\cdots\)
77.2.b.b \(4\) \(0.615\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{3}q^{5}+(2\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots\)