Properties

Label 8031.2.a
Level 8031
Weight 2
Character orbit a
Rep. character \(\chi_{8031}(1,\cdot)\)
Character field \(\Q\)
Dimension 447
Newforms 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: \(\Q\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8031))\) into irreducible Hecke orbits

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

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