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Properties

Label 8031.2.a
Level $8031$
Weight $2$
Character orbit 8031.a
Rep. character $\chi_{8031}(1,\cdot)$
Character field $\Q$
Dimension $447$
Newform subspaces $4$
Sturm bound $1785$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 8031 = 3 \cdot 2677 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8031.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1785\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8031))\).

Total New Old
Modular forms 894 447 447
Cusp forms 891 447 444
Eisenstein series 3 0 3

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

\(3\)\(2677\)FrickeDim
\(+\)\(+\)$+$\(102\)
\(+\)\(-\)$-$\(121\)
\(-\)\(+\)$-$\(132\)
\(-\)\(-\)$+$\(92\)
Plus space\(+\)\(194\)
Minus space\(-\)\(253\)

Trace form

\( 447 q - q^{2} + q^{3} + 445 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{8} + 447 q^{9} + O(q^{10}) \) \( 447 q - q^{2} + q^{3} + 445 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{8} + 447 q^{9} - 2 q^{10} + 4 q^{11} + 7 q^{12} + 14 q^{13} - 8 q^{14} - 2 q^{15} + 437 q^{16} + 18 q^{17} - q^{18} + 12 q^{19} - 6 q^{20} + 4 q^{21} - 8 q^{22} - 3 q^{24} + 449 q^{25} - 22 q^{26} + q^{27} - 16 q^{28} - 2 q^{29} - 6 q^{30} - 12 q^{31} - 49 q^{32} - 4 q^{33} - 14 q^{34} - 8 q^{35} + 445 q^{36} + 6 q^{37} - 24 q^{38} + 14 q^{39} - 14 q^{40} + 26 q^{41} + 8 q^{43} + 6 q^{45} - 48 q^{46} - q^{48} + 475 q^{49} + q^{50} - 2 q^{51} + 42 q^{52} + 10 q^{53} - 3 q^{54} + 12 q^{55} - 8 q^{56} + 12 q^{57} + 10 q^{58} - 16 q^{59} - 26 q^{60} + 22 q^{61} + 401 q^{64} + 40 q^{65} - 12 q^{66} + 8 q^{67} + 106 q^{68} - 4 q^{69} - 48 q^{70} - 16 q^{71} - 9 q^{72} + 26 q^{73} + 6 q^{74} + 7 q^{75} - 8 q^{76} + 44 q^{77} - 6 q^{78} - 24 q^{79} + 46 q^{80} + 447 q^{81} + 14 q^{82} - 16 q^{83} + 4 q^{84} + 12 q^{85} - 48 q^{86} - 2 q^{87} - 40 q^{88} + 10 q^{89} - 2 q^{90} + 12 q^{91} + 4 q^{92} - 4 q^{93} - 16 q^{94} - 56 q^{95} - 39 q^{96} - 22 q^{97} + 39 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8031))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 2677
8031.2.a.a 8031.a 1.a $92$ $64.128$ None \(-6\) \(92\) \(-18\) \(-42\) $-$ $-$ $\mathrm{SU}(2)$
8031.2.a.b 8031.a 1.a $102$ $64.128$ None \(-6\) \(-102\) \(-20\) \(12\) $+$ $+$ $\mathrm{SU}(2)$
8031.2.a.c 8031.a 1.a $121$ $64.128$ None \(7\) \(-121\) \(24\) \(-14\) $+$ $-$ $\mathrm{SU}(2)$
8031.2.a.d 8031.a 1.a $132$ $64.128$ None \(4\) \(132\) \(20\) \(44\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8031))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8031)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2677))\)\(^{\oplus 2}\)