Properties

Label 6031.2.a
Level 6031
Weight 2
Character orbit a
Rep. character \(\chi_{6031}(1,\cdot)\)
Character field \(\Q\)
Dimension 487
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 5 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6031))\) into newform subspaces

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

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