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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19
76.4.a.a \(2\) \(4.484\) \(\Q(\sqrt{33}) \) None \(0\) \(-5\) \(-5\) \(-30\) \(-\) \(+\) \(q+(-2-\beta )q^{3}+(-5+5\beta )q^{5}+(-13+\cdots)q^{7}+\cdots\)
76.4.a.b \(3\) \(4.484\) 3.3.35529.1 None \(0\) \(1\) \(9\) \(44\) \(-\) \(-\) \(q+(\beta _{1}+\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(15-\beta _{1}+\cdots)q^{7}+\cdots\)

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

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