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Properties

Label 76.8.e
Level $76$
Weight $8$
Character orbit 76.e
Rep. character $\chi_{76}(45,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $22$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 8 \)
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: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(76, [\chi])\).

Total New Old
Modular forms 146 22 124
Cusp forms 134 22 112
Eisenstein series 12 0 12

Trace form

\( 22 q + 13 q^{3} + q^{5} + 560 q^{7} - 6002 q^{9} + O(q^{10}) \) \( 22 q + 13 q^{3} + q^{5} + 560 q^{7} - 6002 q^{9} + 472 q^{11} - 567 q^{13} + 2995 q^{15} + 5589 q^{17} + 80912 q^{19} + 44412 q^{21} - 15425 q^{23} - 32806 q^{25} + 50290 q^{27} - 18919 q^{29} + 150296 q^{31} + 314618 q^{33} + 92808 q^{35} + 350100 q^{37} + 948810 q^{39} + 698891 q^{41} + 402545 q^{43} + 1477508 q^{45} - 653621 q^{47} - 1938490 q^{49} - 1386401 q^{51} - 106763 q^{53} + 414508 q^{55} + 1267563 q^{57} + 3136737 q^{59} + 2004581 q^{61} + 1465000 q^{63} - 7397638 q^{65} + 4344391 q^{67} + 1732238 q^{69} - 133823 q^{71} - 8349685 q^{73} - 12136824 q^{75} + 9147480 q^{77} - 94679 q^{79} - 838595 q^{81} - 2884080 q^{83} - 1421409 q^{85} - 31740598 q^{87} - 7039347 q^{89} + 1520096 q^{91} - 1993628 q^{93} + 1707587 q^{95} + 13308115 q^{97} + 6011488 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.8.e.a 76.e 19.c $22$ $23.741$ None \(0\) \(13\) \(1\) \(560\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{8}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(76, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)