Properties

Label 3022.2.a
Level 3022
Weight 2
Character orbit a
Rep. character \(\chi_{3022}(1,\cdot)\)
Character field \(\Q\)
Dimension 125
Newform subspaces 4
Sturm bound 756
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 3022 = 2 \cdot 1511 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3022.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(756\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3022))\).

Total New Old
Modular forms 380 125 255
Cusp forms 377 125 252
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.

\(2\)\(1511\)FrickeDim.
\(+\)\(+\)\(+\)\(28\)
\(+\)\(-\)\(-\)\(35\)
\(-\)\(+\)\(-\)\(34\)
\(-\)\(-\)\(+\)\(28\)
Plus space\(+\)\(56\)
Minus space\(-\)\(69\)

Trace form

\( 125q - q^{2} + 125q^{4} - 2q^{5} - 4q^{6} - 8q^{7} - q^{8} + 117q^{9} + O(q^{10}) \) \( 125q - q^{2} + 125q^{4} - 2q^{5} - 4q^{6} - 8q^{7} - q^{8} + 117q^{9} - 6q^{10} - 6q^{11} - 10q^{13} - 8q^{14} - 4q^{15} + 125q^{16} + 2q^{17} - 13q^{18} - 16q^{19} - 2q^{20} - 8q^{21} - 10q^{22} + 4q^{23} - 4q^{24} + 107q^{25} - 10q^{26} + 12q^{27} - 8q^{28} - 12q^{30} + 4q^{31} - q^{32} + 4q^{33} - 10q^{34} - 16q^{35} + 117q^{36} + 8q^{37} - 44q^{39} - 6q^{40} + 6q^{41} - 8q^{42} - 34q^{43} - 6q^{44} - 18q^{45} - 16q^{46} + 8q^{47} + 93q^{49} - 7q^{50} - 36q^{51} - 10q^{52} - 16q^{54} - 12q^{55} - 8q^{56} + 4q^{57} - 16q^{58} - 2q^{59} - 4q^{60} - 30q^{61} - 4q^{62} - 36q^{63} + 125q^{64} + 4q^{65} - 24q^{66} + 10q^{67} + 2q^{68} - 4q^{69} - 16q^{70} + 36q^{71} - 13q^{72} + 2q^{73} - 16q^{74} + 44q^{75} - 16q^{76} + 28q^{77} + 20q^{78} - 52q^{79} - 2q^{80} + 101q^{81} + 2q^{82} + 26q^{83} - 8q^{84} - 12q^{85} - 2q^{86} - 12q^{87} - 10q^{88} - 10q^{89} - 22q^{90} - 24q^{91} + 4q^{92} + 12q^{93} - 20q^{94} + 44q^{95} - 4q^{96} - 10q^{97} - 17q^{98} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3022))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 1511
3022.2.a.a \(28\) \(24.131\) None \(-28\) \(-3\) \(-10\) \(-1\) \(+\) \(+\)
3022.2.a.b \(28\) \(24.131\) None \(28\) \(-9\) \(-16\) \(-23\) \(-\) \(-\)
3022.2.a.c \(34\) \(24.131\) None \(34\) \(7\) \(12\) \(15\) \(-\) \(+\)
3022.2.a.d \(35\) \(24.131\) None \(-35\) \(5\) \(12\) \(1\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3022))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1511))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database