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Properties

Label 6042.2.a
Level $6042$
Weight $2$
Character orbit 6042.a
Rep. character $\chi_{6042}(1,\cdot)$
Character field $\Q$
Dimension $157$
Newform subspaces $34$
Sturm bound $2160$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6042.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 34 \)
Sturm bound: \(2160\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6042))\).

Total New Old
Modular forms 1088 157 931
Cusp forms 1073 157 916
Eisenstein series 15 0 15

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

\(2\)\(3\)\(19\)\(53\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(12\)
\(+\)\(+\)\(+\)\(-\)$-$\(9\)
\(+\)\(+\)\(-\)\(+\)$-$\(6\)
\(+\)\(+\)\(-\)\(-\)$+$\(12\)
\(+\)\(-\)\(+\)\(+\)$-$\(11\)
\(+\)\(-\)\(+\)\(-\)$+$\(8\)
\(+\)\(-\)\(-\)\(+\)$+$\(7\)
\(+\)\(-\)\(-\)\(-\)$-$\(13\)
\(-\)\(+\)\(+\)\(+\)$-$\(10\)
\(-\)\(+\)\(+\)\(-\)$+$\(9\)
\(-\)\(+\)\(-\)\(+\)$+$\(11\)
\(-\)\(+\)\(-\)\(-\)$-$\(9\)
\(-\)\(-\)\(+\)\(+\)$+$\(7\)
\(-\)\(-\)\(+\)\(-\)$-$\(14\)
\(-\)\(-\)\(-\)\(+\)$-$\(14\)
\(-\)\(-\)\(-\)\(-\)$+$\(5\)
Plus space\(+\)\(71\)
Minus space\(-\)\(86\)

Trace form

\( 157 q + q^{2} + q^{3} + 157 q^{4} - 2 q^{5} + q^{6} + q^{8} + 157 q^{9} + O(q^{10}) \) \( 157 q + q^{2} + q^{3} + 157 q^{4} - 2 q^{5} + q^{6} + q^{8} + 157 q^{9} + 6 q^{10} + 4 q^{11} + q^{12} + 14 q^{13} + 8 q^{14} + 6 q^{15} + 157 q^{16} + 10 q^{17} + q^{18} - 3 q^{19} - 2 q^{20} + 8 q^{21} + 12 q^{22} + 16 q^{23} + q^{24} + 179 q^{25} + 14 q^{26} + q^{27} + 30 q^{29} - 2 q^{30} + 16 q^{31} + q^{32} + 12 q^{33} + 2 q^{34} - 16 q^{35} + 157 q^{36} - 10 q^{37} + q^{38} - 2 q^{39} + 6 q^{40} - 6 q^{41} + 8 q^{42} + 36 q^{43} + 4 q^{44} - 2 q^{45} + 8 q^{46} - 8 q^{47} + q^{48} + 205 q^{49} + 31 q^{50} + 18 q^{51} + 14 q^{52} + q^{53} + q^{54} - 8 q^{55} + 8 q^{56} + q^{57} + 22 q^{58} + 12 q^{59} + 6 q^{60} - 2 q^{61} - 32 q^{62} + 157 q^{64} - 44 q^{65} - 4 q^{66} + 36 q^{67} + 10 q^{68} + 8 q^{69} - 8 q^{71} + q^{72} - 46 q^{73} - 10 q^{74} - q^{75} - 3 q^{76} - 96 q^{77} + 14 q^{78} - 16 q^{79} - 2 q^{80} + 157 q^{81} + 10 q^{82} + 12 q^{83} + 8 q^{84} - 4 q^{85} - 36 q^{86} - 34 q^{87} + 12 q^{88} - 6 q^{89} + 6 q^{90} - 32 q^{91} + 16 q^{92} - 16 q^{94} - 2 q^{95} + q^{96} - 14 q^{97} + 25 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6042))\) 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 3 19 53
6042.2.a.a 6042.a 1.a $1$ $48.246$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
6042.2.a.b 6042.a 1.a $1$ $48.246$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
6042.2.a.c 6042.a 1.a $1$ $48.246$ \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
6042.2.a.d 6042.a 1.a $1$ $48.246$ \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
6042.2.a.e 6042.a 1.a $1$ $48.246$ \(\Q\) None \(-1\) \(1\) \(-3\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
6042.2.a.f 6042.a 1.a $1$ $48.246$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
6042.2.a.g 6042.a 1.a $1$ $48.246$ \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
6042.2.a.h 6042.a 1.a $1$ $48.246$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
6042.2.a.i 6042.a 1.a $1$ $48.246$ \(\Q\) None \(-1\) \(1\) \(3\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+2q^{7}+\cdots\)
6042.2.a.j 6042.a 1.a $1$ $48.246$ \(\Q\) None \(1\) \(-1\) \(2\) \(-4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-4q^{7}+\cdots\)
6042.2.a.k 6042.a 1.a $1$ $48.246$ \(\Q\) None \(1\) \(1\) \(1\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
6042.2.a.l 6042.a 1.a $1$ $48.246$ \(\Q\) None \(1\) \(1\) \(2\) \(1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
6042.2.a.m 6042.a 1.a $1$ $48.246$ \(\Q\) None \(1\) \(1\) \(2\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
6042.2.a.n 6042.a 1.a $1$ $48.246$ \(\Q\) None \(1\) \(1\) \(3\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}-q^{7}+\cdots\)
6042.2.a.o 6042.a 1.a $2$ $48.246$ \(\Q(\sqrt{33}) \) None \(2\) \(-2\) \(-3\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
6042.2.a.p 6042.a 1.a $2$ $48.246$ \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(1\) \(-1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}-\beta q^{7}+\cdots\)
6042.2.a.q 6042.a 1.a $3$ $48.246$ 3.3.257.1 None \(-3\) \(-3\) \(-3\) \(-1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta _{2})q^{5}+q^{6}+\cdots\)
6042.2.a.r 6042.a 1.a $3$ $48.246$ 3.3.788.1 None \(3\) \(-3\) \(2\) \(6\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(\beta _{1}+\beta _{2})q^{5}-q^{6}+\cdots\)
6042.2.a.s 6042.a 1.a $3$ $48.246$ \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-7\) \(-7\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2-\beta _{1})q^{5}+q^{6}+\cdots\)
6042.2.a.t 6042.a 1.a $4$ $48.246$ 4.4.17609.1 None \(4\) \(-4\) \(6\) \(3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(2-\beta _{3})q^{5}-q^{6}+\cdots\)
6042.2.a.u 6042.a 1.a $5$ $48.246$ 5.5.14377697.1 None \(5\) \(-5\) \(2\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{2}q^{7}+\cdots\)
6042.2.a.v 6042.a 1.a $6$ $48.246$ 6.6.21848308.1 None \(-6\) \(6\) \(3\) \(-7\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta _{4}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6042.2.a.w 6042.a 1.a $6$ $48.246$ 6.6.326108912.1 None \(6\) \(-6\) \(-1\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta _{3}q^{5}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
6042.2.a.x 6042.a 1.a $6$ $48.246$ 6.6.48689336.1 None \(6\) \(6\) \(-8\) \(-6\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1})q^{5}+q^{6}+\cdots\)
6042.2.a.y 6042.a 1.a $7$ $48.246$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(7\) \(4\) \(-9\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
6042.2.a.z 6042.a 1.a $9$ $48.246$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-9\) \(-1\) \(4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{6}q^{5}+q^{6}-\beta _{3}q^{7}+\cdots\)
6042.2.a.ba 6042.a 1.a $9$ $48.246$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(9\) \(2\) \(10\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta _{6}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)
6042.2.a.bb 6042.a 1.a $9$ $48.246$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-9\) \(-5\) \(-5\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta _{2})q^{5}-q^{6}+\cdots\)
6042.2.a.bc 6042.a 1.a $9$ $48.246$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-9\) \(-3\) \(-7\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6042.2.a.bd 6042.a 1.a $11$ $48.246$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(-11\) \(2\) \(-2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+\beta _{5}q^{7}+\cdots\)
6042.2.a.be 6042.a 1.a $12$ $48.246$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-12\) \(-3\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+\beta _{10}q^{7}+\cdots\)
6042.2.a.bf 6042.a 1.a $12$ $48.246$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(12\) \(-7\) \(5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
6042.2.a.bg 6042.a 1.a $12$ $48.246$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(12\) \(5\) \(6\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
6042.2.a.bh 6042.a 1.a $13$ $48.246$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(13\) \(13\) \(3\) \(12\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6042))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6042)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(106))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(159))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(318))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1007))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3021))\)\(^{\oplus 2}\)