Properties

Label 6020.2.a
Level 6020
Weight 2
Character orbit a
Rep. character \(\chi_{6020}(1,\cdot)\)
Character field \(\Q\)
Dimension 84
Newforms 11
Sturm bound 2112
Trace bound 11

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Defining parameters

Level: \( N \) = \( 6020 = 2^{2} \cdot 5 \cdot 7 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6020.a (trivial)
Character field: \(\Q\)
Newforms: \( 11 \)
Sturm bound: \(2112\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6020))\).

Total New Old
Modular forms 1068 84 984
Cusp forms 1045 84 961
Eisenstein series 23 0 23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(7\)\(43\)FrickeDim.
\(-\)\(+\)\(+\)\(+\)\(-\)\(13\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(9\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(13\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(13\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(32\)
Minus space\(-\)\(52\)

Trace form

\(84q \) \(\mathstrut +\mathstrut 88q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(84q \) \(\mathstrut +\mathstrut 88q^{9} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 84q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 36q^{29} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut +\mathstrut 84q^{49} \) \(\mathstrut +\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 24q^{57} \) \(\mathstrut -\mathstrut 16q^{59} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 8q^{73} \) \(\mathstrut -\mathstrut 12q^{79} \) \(\mathstrut +\mathstrut 116q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 12q^{85} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 40q^{89} \) \(\mathstrut +\mathstrut 12q^{91} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 36q^{97} \) \(\mathstrut +\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6020))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7 43
6020.2.a.a \(1\) \(48.070\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{3}-q^{5}+q^{7}-2q^{9}-5q^{11}+q^{13}+\cdots\)
6020.2.a.b \(1\) \(48.070\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{3}-q^{5}+q^{7}-2q^{9}+3q^{11}+5q^{13}+\cdots\)
6020.2.a.c \(1\) \(48.070\) \(\Q\) None \(0\) \(2\) \(1\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+2q^{3}+q^{5}+q^{7}+q^{9}+5q^{11}-5q^{13}+\cdots\)
6020.2.a.d \(7\) \(48.070\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-3\) \(7\) \(7\) \(-\) \(-\) \(-\) \(-\) \(q-\beta _{4}q^{3}+q^{5}+q^{7}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots\)
6020.2.a.e \(7\) \(48.070\) 7.7.187391161.1 None \(0\) \(-1\) \(-7\) \(-7\) \(-\) \(+\) \(+\) \(-\) \(q-\beta _{5}q^{3}-q^{5}-q^{7}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{9}+\cdots\)
6020.2.a.f \(8\) \(48.070\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-5\) \(-8\) \(8\) \(-\) \(+\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{3}-q^{5}+q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
6020.2.a.g \(9\) \(48.070\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(9\) \(-9\) \(-\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}+q^{5}-q^{7}+(1+\beta _{2})q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots\)
6020.2.a.h \(12\) \(48.070\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(-12\) \(12\) \(-\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{3}-q^{5}+q^{7}+(2+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6020.2.a.i \(12\) \(48.070\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(12\) \(12\) \(-\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+q^{5}+q^{7}+(2+\beta _{2})q^{9}+\beta _{6}q^{11}+\cdots\)
6020.2.a.j \(13\) \(48.070\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-1\) \(-13\) \(-13\) \(-\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}-q^{5}-q^{7}+(1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
6020.2.a.k \(13\) \(48.070\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(0\) \(13\) \(-13\) \(-\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{3}+q^{5}-q^{7}+(1+\beta _{2})q^{9}+\beta _{8}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6020))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(172))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(215))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(301))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(430))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(602))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(860))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1204))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1505))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3010))\)\(^{\oplus 2}\)