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 $1$

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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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
77.2.b.a 77.b 77.b $2$ $0.615$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{2}-5q^{4}-\beta q^{7}+3\beta q^{8}+3q^{9}+\cdots\)
77.2.b.b 77.b 77.b $4$ $0.615$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{3}q^{3}-\beta _{3}q^{5}+(2\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots\)