Properties

Label 76.7.h
Level $76$
Weight $7$
Character orbit 76.h
Rep. character $\chi_{76}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
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 126 20 106
Cusp forms 114 20 94
Eisenstein series 12 0 12

Trace form

\( 20q - 30q^{3} - 56q^{5} + 464q^{7} + 2200q^{9} + O(q^{10}) \) \( 20q - 30q^{3} - 56q^{5} + 464q^{7} + 2200q^{9} - 3644q^{11} - 7140q^{13} + 9168q^{15} + 1132q^{17} + 2110q^{19} - 8748q^{21} + 832q^{23} - 27698q^{25} - 10920q^{29} - 30306q^{33} + 4172q^{35} + 81144q^{39} + 109206q^{41} + 110740q^{43} - 785440q^{45} + 107080q^{47} + 136092q^{49} + 199872q^{51} + 254796q^{53} + 354840q^{55} + 212268q^{57} - 610638q^{59} + 47864q^{61} - 254476q^{63} - 839562q^{67} + 366660q^{71} + 854482q^{73} + 763088q^{77} + 1718592q^{79} - 1054142q^{81} + 439612q^{83} - 400236q^{85} - 1604736q^{87} + 478032q^{89} + 599856q^{91} + 829380q^{93} - 1055660q^{95} - 191286q^{97} - 2336728q^{99} + O(q^{100}) \)

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.h.a \(20\) \(17.484\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-30\) \(-56\) \(464\) \(q+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-6+6\beta _{3}+\cdots)q^{5}+\cdots\)

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

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