Properties

Label 76.2.e
Level $76$
Weight $2$
Character orbit 76.e
Rep. character $\chi_{76}(45,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $2$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
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 26 2 24
Cusp forms 14 2 12
Eisenstein series 12 0 12

Trace form

\( 2 q + q^{3} + q^{5} + 2 q^{9} + O(q^{10}) \) \( 2 q + q^{3} + q^{5} + 2 q^{9} - 8 q^{11} + q^{13} - q^{15} - 3 q^{17} - 8 q^{19} - 5 q^{23} + 4 q^{25} + 10 q^{27} - 7 q^{29} + 8 q^{31} - 4 q^{33} + 20 q^{37} + 2 q^{39} + 5 q^{41} + 5 q^{43} + 4 q^{45} + 7 q^{47} - 14 q^{49} + 3 q^{51} - 11 q^{53} - 4 q^{55} - q^{57} - 3 q^{59} - 11 q^{61} + 2 q^{65} + 3 q^{67} - 10 q^{69} - 11 q^{71} - 15 q^{73} + 8 q^{75} + 13 q^{79} - q^{81} + 3 q^{85} - 14 q^{87} - 3 q^{89} + 4 q^{93} - q^{95} + 5 q^{97} - 8 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.2.e.a $2$ $0.607$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(0\) \(q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)

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

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