Properties

Label 76.3.g
Level $76$
Weight $3$
Character orbit 76.g
Rep. character $\chi_{76}(7,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
Newform subspaces $3$
Sturm bound $30$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(30\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 44 44 0
Cusp forms 36 36 0
Eisenstein series 8 8 0

Trace form

\( 36q - q^{2} - 3q^{4} - 2q^{5} - 15q^{6} + 2q^{8} + 36q^{9} + O(q^{10}) \) \( 36q - q^{2} - 3q^{4} - 2q^{5} - 15q^{6} + 2q^{8} + 36q^{9} + 8q^{10} - 22q^{12} + 6q^{13} + 18q^{14} + 13q^{16} - 26q^{17} - 28q^{18} - 76q^{20} - 8q^{21} + 33q^{22} + 17q^{24} - 52q^{25} - 104q^{26} - 42q^{28} - 2q^{29} - 96q^{30} + 19q^{32} + 36q^{33} + 44q^{34} - 2q^{36} - 88q^{37} - 186q^{38} + 30q^{40} + 50q^{41} + 86q^{42} + 225q^{44} + 56q^{45} + 212q^{46} - 113q^{48} - 92q^{49} + 418q^{50} - 54q^{52} + 6q^{53} + 167q^{54} + 276q^{56} - 6q^{57} + 80q^{58} - 182q^{60} - 146q^{61} - 156q^{62} + 438q^{64} - 164q^{65} - 45q^{66} + 140q^{68} - 428q^{69} + 36q^{70} - 294q^{72} - 134q^{73} - 232q^{74} + 483q^{76} + 352q^{77} + 152q^{78} - 110q^{80} + 334q^{81} - 357q^{82} - 100q^{84} + 346q^{85} + 22q^{86} - 718q^{88} + 118q^{89} - 64q^{90} - 540q^{92} + 184q^{93} - 488q^{94} - 506q^{96} - 374q^{97} + 271q^{98} + O(q^{100}) \)

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.g.a \(4\) \(2.071\) \(\Q(\sqrt{-3}, \sqrt{-10})\) None \(-4\) \(6\) \(-4\) \(0\) \(q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots\)
76.3.g.b \(4\) \(2.071\) \(\Q(\sqrt{-3}, \sqrt{-10})\) None \(8\) \(-6\) \(-4\) \(0\) \(q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots\)
76.3.g.c \(28\) \(2.071\) None \(-5\) \(0\) \(6\) \(0\)