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

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

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

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