Properties

Label 6019.2.a
Level 6019
Weight 2
Character orbit a
Rep. character \(\chi_{6019}(1,\cdot)\)
Character field \(\Q\)
Dimension 463
Newforms 5
Sturm bound 1082
Trace bound 1

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Defining parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(1082\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6019))\).

Total New Old
Modular forms 542 463 79
Cusp forms 539 463 76
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.

\(13\)\(463\)FrickeDim.
\(+\)\(+\)\(+\)\(108\)
\(+\)\(-\)\(-\)\(123\)
\(-\)\(+\)\(-\)\(130\)
\(-\)\(-\)\(+\)\(102\)
Plus space\(+\)\(210\)
Minus space\(-\)\(253\)

Trace form

\(463q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 461q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 463q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(463q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 461q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 463q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 461q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 30q^{20} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 473q^{25} \) \(\mathstrut +\mathstrut 3q^{26} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 12q^{28} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 16q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 5q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 54q^{34} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 473q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 38q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 28q^{44} \) \(\mathstrut +\mathstrut 66q^{45} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 56q^{48} \) \(\mathstrut +\mathstrut 495q^{49} \) \(\mathstrut +\mathstrut 51q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 46q^{53} \) \(\mathstrut -\mathstrut 16q^{54} \) \(\mathstrut +\mathstrut 56q^{55} \) \(\mathstrut +\mathstrut 36q^{56} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 36q^{60} \) \(\mathstrut +\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut +\mathstrut 421q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut -\mathstrut 56q^{66} \) \(\mathstrut +\mathstrut 16q^{67} \) \(\mathstrut -\mathstrut 42q^{68} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 80q^{70} \) \(\mathstrut +\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 39q^{72} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 16q^{75} \) \(\mathstrut -\mathstrut 92q^{76} \) \(\mathstrut +\mathstrut 64q^{77} \) \(\mathstrut -\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 46q^{80} \) \(\mathstrut +\mathstrut 487q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 36q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 130q^{90} \) \(\mathstrut +\mathstrut 28q^{92} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 76q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut +\mathstrut 34q^{97} \) \(\mathstrut -\mathstrut 111q^{98} \) \(\mathstrut +\mathstrut 48q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6019))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 13 463
6019.2.a.a \(1\) \(48.062\) \(\Q\) None \(0\) \(0\) \(3\) \(-3\) \(-\) \(-\) \(q-2q^{4}+3q^{5}-3q^{7}-3q^{9}-q^{11}+\cdots\)
6019.2.a.b \(101\) \(48.062\) None \(-8\) \(-13\) \(-43\) \(-1\) \(-\) \(-\)
6019.2.a.c \(108\) \(48.062\) None \(-11\) \(1\) \(-40\) \(-8\) \(+\) \(+\)
6019.2.a.d \(123\) \(48.062\) None \(10\) \(1\) \(46\) \(12\) \(+\) \(-\)
6019.2.a.e \(130\) \(48.062\) None \(10\) \(11\) \(40\) \(8\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6019))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6019)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(463))\)\(^{\oplus 2}\)