Properties

Label 6031.2.a
Level 6031
Weight 2
Character orbit a
Rep. character \(\chi_{6031}(1,\cdot)\)
Character field \(\Q\)
Dimension 487
Newforms 5
Sturm bound 1038
Trace bound 1

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Defining parameters

Level: \( N \) = \( 6031 = 37 \cdot 163 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6031.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(1038\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6031))\).

Total New Old
Modular forms 520 487 33
Cusp forms 517 487 30
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.

\(37\)\(163\)FrickeDim.
\(+\)\(+\)\(+\)\(110\)
\(+\)\(-\)\(-\)\(133\)
\(-\)\(+\)\(-\)\(135\)
\(-\)\(-\)\(+\)\(109\)
Plus space\(+\)\(219\)
Minus space\(-\)\(268\)

Trace form

\(487q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 485q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 491q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(487q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 485q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 491q^{9} \) \(\mathstrut -\mathstrut 14q^{10} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 24q^{15} \) \(\mathstrut +\mathstrut 461q^{16} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 23q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 26q^{20} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 16q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 477q^{25} \) \(\mathstrut +\mathstrut 18q^{26} \) \(\mathstrut +\mathstrut 40q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 16q^{30} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 23q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 42q^{34} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 433q^{36} \) \(\mathstrut +\mathstrut q^{37} \) \(\mathstrut +\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 36q^{39} \) \(\mathstrut -\mathstrut 46q^{40} \) \(\mathstrut +\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 60q^{42} \) \(\mathstrut -\mathstrut 14q^{43} \) \(\mathstrut -\mathstrut 24q^{44} \) \(\mathstrut +\mathstrut 38q^{45} \) \(\mathstrut +\mathstrut 32q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut +\mathstrut 511q^{49} \) \(\mathstrut +\mathstrut q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 26q^{52} \) \(\mathstrut -\mathstrut 4q^{53} \) \(\mathstrut +\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 56q^{55} \) \(\mathstrut -\mathstrut 28q^{56} \) \(\mathstrut -\mathstrut 32q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 16q^{59} \) \(\mathstrut -\mathstrut 32q^{60} \) \(\mathstrut -\mathstrut 8q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 445q^{64} \) \(\mathstrut -\mathstrut 60q^{65} \) \(\mathstrut +\mathstrut 72q^{66} \) \(\mathstrut +\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 26q^{71} \) \(\mathstrut +\mathstrut 63q^{72} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut -\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 36q^{76} \) \(\mathstrut +\mathstrut 36q^{77} \) \(\mathstrut +\mathstrut 36q^{78} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 511q^{81} \) \(\mathstrut +\mathstrut 6q^{82} \) \(\mathstrut +\mathstrut 30q^{83} \) \(\mathstrut +\mathstrut 12q^{84} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 68q^{86} \) \(\mathstrut -\mathstrut 12q^{87} \) \(\mathstrut -\mathstrut 48q^{88} \) \(\mathstrut +\mathstrut 18q^{89} \) \(\mathstrut +\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut +\mathstrut 40q^{93} \) \(\mathstrut -\mathstrut 96q^{94} \) \(\mathstrut +\mathstrut 56q^{95} \) \(\mathstrut -\mathstrut 60q^{96} \) \(\mathstrut -\mathstrut 60q^{97} \) \(\mathstrut +\mathstrut 43q^{98} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6031))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 37 163
6031.2.a.a \(1\) \(48.158\) \(\Q\) None \(0\) \(3\) \(4\) \(1\) \(-\) \(+\) \(q+3q^{3}-2q^{4}+4q^{5}+q^{7}+6q^{9}+\cdots\)
6031.2.a.b \(109\) \(48.158\) None \(-11\) \(-14\) \(-28\) \(-16\) \(-\) \(-\)
6031.2.a.c \(110\) \(48.158\) None \(-9\) \(0\) \(-26\) \(-4\) \(+\) \(+\)
6031.2.a.d \(133\) \(48.158\) None \(14\) \(8\) \(34\) \(8\) \(+\) \(-\)
6031.2.a.e \(134\) \(48.158\) None \(9\) \(7\) \(22\) \(11\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6031))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6031)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(163))\)\(^{\oplus 2}\)