Properties

Label 8031.2.a
Level 8031
Weight 2
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 2677
8031.2.a.a \(92\) \(64.128\) None \(-6\) \(92\) \(-18\) \(-42\) \(-\) \(-\)
8031.2.a.b \(102\) \(64.128\) None \(-6\) \(-102\) \(-20\) \(12\) \(+\) \(+\)
8031.2.a.c \(121\) \(64.128\) None \(7\) \(-121\) \(24\) \(-14\) \(+\) \(-\)
8031.2.a.d \(132\) \(64.128\) None \(4\) \(132\) \(20\) \(44\) \(-\) \(+\)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database