Properties

Label 77.2.l
Level $77$
Weight $2$
Character orbit 77.l
Rep. character $\chi_{77}(6,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $24$
Newform subspaces $2$
Sturm bound $16$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 77 = 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 77.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
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 40 40 0
Cusp forms 24 24 0
Eisenstein series 16 16 0

Trace form

\( 24q - 10q^{2} - 10q^{7} + 2q^{9} + O(q^{10}) \) \( 24q - 10q^{2} - 10q^{7} + 2q^{9} - 2q^{11} - 13q^{14} - 6q^{16} - 35q^{18} + 28q^{22} + 8q^{23} - 40q^{25} + 25q^{28} + 10q^{29} - 40q^{30} + 40q^{35} + 50q^{36} - 14q^{37} + 30q^{39} + 50q^{42} + 15q^{44} + 5q^{46} + 22q^{49} - 60q^{50} - 10q^{51} + 30q^{53} - 46q^{56} - 90q^{57} + 17q^{58} + 120q^{60} - 20q^{63} - 72q^{64} + 4q^{67} - 104q^{71} - 45q^{72} + 90q^{74} - 12q^{77} - 20q^{78} + 10q^{79} - 34q^{81} - 70q^{84} + 80q^{85} + 29q^{86} - 94q^{88} - 30q^{91} + 45q^{92} - 40q^{93} - 60q^{95} + 84q^{99} + O(q^{100}) \)

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.l.a \(8\) \(0.615\) 8.0.37515625.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+(1-\beta _{1}+\beta _{3}+\beta _{4}+\beta _{5}-\beta _{6})q^{2}+\cdots\)
77.2.l.b \(16\) \(0.615\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-10\) \(0\) \(0\) \(-10\) \(q+(-1-\beta _{9}-\beta _{11})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)