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Properties

Label 76.4.e
Level $76$
Weight $4$
Character orbit 76.e
Rep. character $\chi_{76}(45,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(76, [\chi])\).

Total New Old
Modular forms 66 10 56
Cusp forms 54 10 44
Eisenstein series 12 0 12

Trace form

\( 10 q + 7 q^{3} - 4 q^{5} - 20 q^{7} - 50 q^{9} + O(q^{10}) \) \( 10 q + 7 q^{3} - 4 q^{5} - 20 q^{7} - 50 q^{9} - 50 q^{11} - 56 q^{13} + 10 q^{15} + 32 q^{17} + 77 q^{19} + 126 q^{21} + 184 q^{23} - 121 q^{25} - 218 q^{27} + 352 q^{29} + 264 q^{31} + 83 q^{33} - 132 q^{35} - 640 q^{37} - 324 q^{39} - 57 q^{41} - 528 q^{43} - 232 q^{45} - 434 q^{47} + 2138 q^{49} - 242 q^{51} + 780 q^{53} + 598 q^{55} + 1482 q^{57} - 343 q^{59} + 536 q^{61} - 1568 q^{63} - 1988 q^{65} + 779 q^{67} - 1156 q^{69} + 474 q^{71} + 1453 q^{73} - 2994 q^{75} - 2956 q^{77} - 1968 q^{79} - 1097 q^{81} - 698 q^{83} - 2334 q^{85} + 8372 q^{87} + 380 q^{89} + 1348 q^{91} + 1684 q^{93} + 4312 q^{95} + 883 q^{97} + 5230 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.4.e.a 76.e 19.c $10$ $4.484$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(7\) \(-4\) \(-20\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(\beta _{3}+\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(76, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)