Properties

Label 6022.2.a
Level 6022
Weight 2
Character orbit a
Rep. character \(\chi_{6022}(1,\cdot)\)
Character field \(\Q\)
Dimension 250
Newforms 5
Sturm bound 1506
Trace bound 1

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Defining parameters

Level: \( N \) = \( 6022 = 2 \cdot 3011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6022.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(1506\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6022))\).

Total New Old
Modular forms 755 250 505
Cusp forms 752 250 502
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.

\(2\)\(3011\)FrickeDim.
\(+\)\(+\)\(+\)\(64\)
\(+\)\(-\)\(-\)\(61\)
\(-\)\(+\)\(-\)\(71\)
\(-\)\(-\)\(+\)\(54\)
Plus space\(+\)\(118\)
Minus space\(-\)\(132\)

Trace form

\(250q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 250q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 248q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(250q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 250q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 248q^{9} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 2q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 250q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 8q^{18} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 236q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 20q^{27} \) \(\mathstrut -\mathstrut 18q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 248q^{36} \) \(\mathstrut -\mathstrut 28q^{37} \) \(\mathstrut +\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 242q^{49} \) \(\mathstrut -\mathstrut 8q^{50} \) \(\mathstrut +\mathstrut 40q^{51} \) \(\mathstrut -\mathstrut 8q^{52} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 12q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 28q^{57} \) \(\mathstrut -\mathstrut 2q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut +\mathstrut 250q^{64} \) \(\mathstrut -\mathstrut 36q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 30q^{67} \) \(\mathstrut -\mathstrut 4q^{68} \) \(\mathstrut -\mathstrut 40q^{69} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut -\mathstrut 14q^{74} \) \(\mathstrut -\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 282q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 8q^{84} \) \(\mathstrut -\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut +\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 8q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 28q^{91} \) \(\mathstrut +\mathstrut 28q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut -\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6022))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3011
6022.2.a.a \(3\) \(48.086\) \(\Q(\zeta_{14})^+\) None \(3\) \(-4\) \(-7\) \(-9\) \(-\) \(+\) \(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-3+\beta _{1}+\cdots)q^{5}+\cdots\)
6022.2.a.b \(54\) \(48.086\) None \(54\) \(-22\) \(-14\) \(-20\) \(-\) \(-\)
6022.2.a.c \(61\) \(48.086\) None \(-61\) \(8\) \(16\) \(2\) \(+\) \(-\)
6022.2.a.d \(64\) \(48.086\) None \(-64\) \(-9\) \(-17\) \(-2\) \(+\) \(+\)
6022.2.a.e \(68\) \(48.086\) None \(68\) \(25\) \(20\) \(29\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6022))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(3011))\)\(^{\oplus 2}\)