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

Related objects

Downloads

Learn more about

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

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

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

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