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Properties

Label 76.3.h
Level $76$
Weight $3$
Character orbit 76.h
Rep. character $\chi_{76}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 46 8 38
Cusp forms 34 8 26
Eisenstein series 12 0 12

Trace form

\( 8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9} + O(q^{10}) \) \( 8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9} - 10 q^{11} + 9 q^{13} + 33 q^{15} + 23 q^{17} - 33 q^{19} - 31 q^{23} - 73 q^{25} - 105 q^{29} - 111 q^{33} - 68 q^{35} + 234 q^{39} + 18 q^{41} - 41 q^{43} + 200 q^{45} + 107 q^{47} + 312 q^{49} - 9 q^{51} + 39 q^{53} + 70 q^{55} - 381 q^{57} + 348 q^{59} - 45 q^{61} - 358 q^{63} - 432 q^{67} - 243 q^{71} + 16 q^{73} + 544 q^{77} + 75 q^{79} - 68 q^{81} - 82 q^{83} + 109 q^{85} + 414 q^{87} - 213 q^{89} + 222 q^{91} + 288 q^{93} - 385 q^{95} + 144 q^{97} - 388 q^{99} + O(q^{100}) \)

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.h.a 76.h 19.d $8$ $2.071$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(6\) \(-1\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{5}-\beta _{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(76, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)