Properties

Label 6023.2.a
Level 6023
Weight 2
Character orbit a
Rep. character \(\chi_{6023}(1,\cdot)\)
Character field \(\Q\)
Dimension 475
Newforms 4
Sturm bound 1060
Trace bound 1

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Defining parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(1060\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6023))\).

Total New Old
Modular forms 532 475 57
Cusp forms 529 475 54
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.

\(19\)\(317\)FrickeDim.
\(+\)\(+\)\(+\)\(99\)
\(+\)\(-\)\(-\)\(140\)
\(-\)\(+\)\(-\)\(138\)
\(-\)\(-\)\(+\)\(98\)
Plus space\(+\)\(197\)
Minus space\(-\)\(278\)

Trace form

\( 475q + 3q^{2} + 4q^{3} + 481q^{4} + 4q^{6} + 6q^{7} + 15q^{8} + 471q^{9} + O(q^{10}) \) \( 475q + 3q^{2} + 4q^{3} + 481q^{4} + 4q^{6} + 6q^{7} + 15q^{8} + 471q^{9} + 18q^{10} + 2q^{11} + 8q^{12} + 14q^{13} - 20q^{14} + 16q^{15} + 489q^{16} + 8q^{17} + 3q^{18} - 3q^{19} + 6q^{20} - 24q^{21} + 36q^{22} + 16q^{23} + 16q^{24} + 503q^{25} + 10q^{26} + 40q^{27} + 16q^{28} - 10q^{29} - 16q^{30} + 8q^{31} + 3q^{32} + 32q^{33} - 10q^{34} + 2q^{35} + 469q^{36} + 26q^{37} + 3q^{38} + 18q^{40} + 10q^{41} - 20q^{42} + 30q^{43} + 28q^{44} + 32q^{45} - 8q^{46} + 2q^{47} + 465q^{49} - 35q^{50} - 24q^{51} + 22q^{52} + 26q^{53} - 40q^{54} - 6q^{55} - 84q^{56} + 4q^{57} + 58q^{58} + 12q^{59} - 112q^{60} + 16q^{61} - 16q^{62} + 22q^{63} + 569q^{64} + 64q^{65} - 36q^{66} + 52q^{67} - 22q^{68} - 8q^{69} - 48q^{70} - 36q^{71} + 7q^{72} + 56q^{73} - 6q^{74} + 84q^{75} - 3q^{76} + 6q^{77} + 44q^{78} + 16q^{79} - 34q^{80} + 467q^{81} + 86q^{82} - 8q^{83} - 44q^{84} + 22q^{85} + 68q^{86} + 36q^{87} + 136q^{88} + 6q^{89} + 82q^{90} + 4q^{91} + 76q^{92} + 52q^{93} + 52q^{94} + 4q^{95} + 60q^{96} + 46q^{97} - 13q^{98} + 22q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6023))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 19 317
6023.2.a.a \(98\) \(48.094\) None \(-8\) \(-25\) \(-10\) \(-18\) \(-\) \(-\)
6023.2.a.b \(99\) \(48.094\) None \(-4\) \(-3\) \(-15\) \(-19\) \(+\) \(+\)
6023.2.a.c \(138\) \(48.094\) None \(11\) \(29\) \(12\) \(18\) \(-\) \(+\)
6023.2.a.d \(140\) \(48.094\) None \(4\) \(3\) \(13\) \(25\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6023))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6023)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(317))\)\(^{\oplus 2}\)