Properties

Label 76.3.b
Level $76$
Weight $3$
Character orbit 76.b
Rep. character $\chi_{76}(39,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $2$
Sturm bound $30$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(76, [\chi])\).

Total New Old
Modular forms 22 18 4
Cusp forms 18 18 0
Eisenstein series 4 0 4

Trace form

\( 18q - 2q^{2} - 6q^{4} - 4q^{5} - 6q^{6} - 8q^{8} - 54q^{9} + O(q^{10}) \) \( 18q - 2q^{2} - 6q^{4} - 4q^{5} - 6q^{6} - 8q^{8} - 54q^{9} - 8q^{10} + 16q^{12} + 12q^{13} + 36q^{14} + 26q^{16} + 20q^{17} + 22q^{18} + 40q^{20} - 16q^{21} - 24q^{22} - 98q^{24} + 46q^{25} + 26q^{26} + 6q^{28} - 4q^{29} - 84q^{30} + 8q^{32} - 48q^{33} - 68q^{34} + 68q^{36} + 76q^{37} - 180q^{40} + 100q^{41} + 202q^{42} + 24q^{44} - 68q^{45} + 52q^{46} + 248q^{48} - 46q^{49} - 190q^{50} - 204q^{52} + 12q^{53} - 146q^{54} + 12q^{56} - 14q^{58} - 52q^{60} - 100q^{61} + 300q^{62} + 138q^{64} - 88q^{65} + 36q^{66} + 58q^{68} - 160q^{69} + 36q^{70} + 192q^{72} - 268q^{73} - 200q^{74} + 296q^{77} + 508q^{78} - 316q^{80} + 242q^{81} - 276q^{82} - 260q^{84} + 176q^{85} - 268q^{86} + 472q^{88} + 20q^{89} + 316q^{90} + 114q^{92} + 80q^{93} - 376q^{94} - 10q^{96} + 260q^{97} - 106q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
76.3.b.a \(4\) \(2.071\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(-4\) \(0\) \(-4\) \(0\) \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
76.3.b.b \(14\) \(2.071\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{5}q^{4}+\beta _{12}q^{5}+\cdots\)