Properties

Label 76.7.j
Level $76$
Weight $7$
Character orbit 76.j
Rep. character $\chi_{76}(13,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $60$
Newform subspaces $1$
Sturm bound $70$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(70\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(76, [\chi])\).

Total New Old
Modular forms 378 60 318
Cusp forms 342 60 282
Eisenstein series 36 0 36

Trace form

\( 60q + 30q^{3} - 216q^{7} + 690q^{9} + O(q^{10}) \) \( 60q + 30q^{3} - 216q^{7} + 690q^{9} + 1680q^{11} - 2940q^{13} + 2496q^{15} - 5112q^{17} - 15792q^{19} - 32076q^{21} - 19272q^{23} + 58896q^{25} - 124830q^{27} + 126840q^{29} + 30780q^{31} - 274470q^{33} - 226284q^{35} + 178968q^{39} + 83394q^{41} + 418848q^{43} - 95472q^{45} - 498696q^{47} - 744330q^{49} + 1334538q^{51} + 458004q^{53} - 260136q^{55} - 981984q^{57} - 523362q^{59} - 644172q^{61} + 926832q^{63} + 1337220q^{65} + 1719114q^{67} + 1333800q^{69} - 1895220q^{71} - 1189704q^{73} + 1337256q^{77} + 147432q^{79} + 272130q^{81} + 442800q^{83} + 1479096q^{85} + 1300572q^{87} - 301596q^{89} + 661008q^{91} + 3576q^{93} - 5709984q^{95} + 1386630q^{97} + 3822798q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
76.7.j.a \(60\) \(17.484\) None \(0\) \(30\) \(0\) \(-216\)

Decomposition of \(S_{7}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(76, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)