Properties

Label 76.2.i
Level $76$
Weight $2$
Character orbit 76.i
Rep. character $\chi_{76}(5,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $12$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.i (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(76, [\chi])\).

Total New Old
Modular forms 78 12 66
Cusp forms 42 12 30
Eisenstein series 36 0 36

Trace form

\( 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9} + O(q^{10}) \) \( 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9} + 3 q^{11} - 9 q^{13} - 15 q^{15} - 3 q^{17} - 12 q^{19} - 15 q^{21} - 12 q^{23} - 18 q^{25} - 9 q^{27} + 27 q^{29} + 6 q^{31} + 48 q^{33} + 33 q^{35} - 12 q^{37} + 60 q^{39} + 3 q^{41} + 27 q^{43} + 24 q^{45} - 15 q^{47} + 9 q^{49} - 33 q^{51} - 21 q^{53} - 27 q^{55} - 42 q^{57} - 48 q^{59} - 6 q^{61} - 9 q^{63} - 33 q^{65} + 24 q^{67} - 33 q^{69} + 30 q^{73} + 42 q^{75} + 24 q^{77} + 3 q^{79} + 3 q^{81} + 3 q^{83} - 42 q^{85} - 18 q^{87} - 18 q^{89} - 24 q^{91} - 78 q^{93} + 9 q^{95} + 12 q^{97} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.2.i.a 76.i 19.e $12$ $0.607$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 76.2.i.a \(0\) \(-3\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1-\beta _{5}+\beta _{7}+\beta _{9}+\beta _{11})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

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