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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 $2$

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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.3.g.a 76.g 76.g $4$ $2.071$ \(\Q(\sqrt{-3}, \sqrt{-10})\) None \(-4\) \(6\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots\)
76.3.g.b 76.g 76.g $4$ $2.071$ \(\Q(\sqrt{-3}, \sqrt{-10})\) None \(8\) \(-6\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots\)
76.3.g.c 76.g 76.g $28$ $2.071$ None \(-5\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$