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Properties

Label 76.4.a
Level $76$
Weight $4$
Character orbit 76.a
Rep. character $\chi_{76}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 76.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(76))\).

Total New Old
Modular forms 33 5 28
Cusp forms 27 5 22
Eisenstein series 6 0 6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(19\)FrickeDim
\(-\)\(+\)$-$\(2\)
\(-\)\(-\)$+$\(3\)
Plus space\(+\)\(3\)
Minus space\(-\)\(2\)

Trace form

\( 5 q - 4 q^{3} + 4 q^{5} + 14 q^{7} + 35 q^{9} + O(q^{10}) \) \( 5 q - 4 q^{3} + 4 q^{5} + 14 q^{7} + 35 q^{9} + 8 q^{11} - 46 q^{13} + 20 q^{15} + 82 q^{17} + 19 q^{19} - 72 q^{21} + 98 q^{23} - 35 q^{25} + 8 q^{27} + 62 q^{29} - 204 q^{31} - 404 q^{33} - 348 q^{35} - 86 q^{37} + 606 q^{39} - 330 q^{41} + 144 q^{43} + 88 q^{45} - 292 q^{47} + 97 q^{49} + 104 q^{51} - 78 q^{53} - 4 q^{55} + 114 q^{57} + 508 q^{59} + 40 q^{61} + 1592 q^{63} + 368 q^{65} + 1588 q^{67} - 2300 q^{69} - 660 q^{71} - 1570 q^{73} - 156 q^{75} + 3250 q^{77} - 2676 q^{79} + 437 q^{81} + 1712 q^{83} - 750 q^{85} - 2474 q^{87} + 1078 q^{89} - 472 q^{91} + 1316 q^{93} + 266 q^{95} + 758 q^{97} + 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(76))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 19
76.4.a.a 76.a 1.a $2$ $4.484$ \(\Q(\sqrt{33}) \) None \(0\) \(-5\) \(-5\) \(-30\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{3}+(-5+5\beta )q^{5}+(-13+\cdots)q^{7}+\cdots\)
76.4.a.b 76.a 1.a $3$ $4.484$ 3.3.35529.1 None \(0\) \(1\) \(9\) \(44\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(15-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(76))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(76)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)