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Properties

Label 6020.2.a
Level $6020$
Weight $2$
Character orbit 6020.a
Rep. character $\chi_{6020}(1,\cdot)$
Character field $\Q$
Dimension $84$
Newform subspaces $11$
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: \(\Q\)
Newform subspaces: \( 11 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6020))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 7 43
6020.2.a.a 6020.a 1.a $1$ $48.070$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}-2q^{9}-5q^{11}+q^{13}+\cdots\)
6020.2.a.b 6020.a 1.a $1$ $48.070$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}-2q^{9}+3q^{11}+5q^{13}+\cdots\)
6020.2.a.c 6020.a 1.a $1$ $48.070$ \(\Q\) None \(0\) \(2\) \(1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{7}+q^{9}+5q^{11}-5q^{13}+\cdots\)
6020.2.a.d 6020.a 1.a $7$ $48.070$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-3\) \(7\) \(7\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{3}+q^{5}+q^{7}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots\)
6020.2.a.e 6020.a 1.a $7$ $48.070$ 7.7.187391161.1 None \(0\) \(-1\) \(-7\) \(-7\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{3}-q^{5}-q^{7}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{9}+\cdots\)
6020.2.a.f 6020.a 1.a $8$ $48.070$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-5\) \(-8\) \(8\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
6020.2.a.g 6020.a 1.a $9$ $48.070$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(9\) \(-9\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}-q^{7}+(1+\beta _{2})q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots\)
6020.2.a.h 6020.a 1.a $12$ $48.070$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(-12\) \(12\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+q^{7}+(2+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6020.2.a.i 6020.a 1.a $12$ $48.070$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(12\) \(12\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+q^{7}+(2+\beta _{2})q^{9}+\beta _{6}q^{11}+\cdots\)
6020.2.a.j 6020.a 1.a $13$ $48.070$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-1\) \(-13\) \(-13\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}-q^{7}+(1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
6020.2.a.k 6020.a 1.a $13$ $48.070$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(0\) \(13\) \(-13\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}-q^{7}+(1+\beta _{2})q^{9}+\beta _{8}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(\Gamma_0(6020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(172))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(215))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(301))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(430))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(602))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(860))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1204))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1505))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3010))\)\(^{\oplus 2}\)