Properties

Label 6042.2.a
Level 6042
Weight 2
Character orbit a
Rep. character \(\chi_{6042}(1,\cdot)\)
Character field \(\Q\)
Dimension 157
Newforms 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: \(\Q\)
Newforms: \( 34 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6042))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 19 53
6042.2.a.a \(1\) \(48.246\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
6042.2.a.b \(1\) \(48.246\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-3\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
6042.2.a.c \(1\) \(48.246\) \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
6042.2.a.d \(1\) \(48.246\) \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
6042.2.a.e \(1\) \(48.246\) \(\Q\) None \(-1\) \(1\) \(-3\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
6042.2.a.f \(1\) \(48.246\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
6042.2.a.g \(1\) \(48.246\) \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
6042.2.a.h \(1\) \(48.246\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
6042.2.a.i \(1\) \(48.246\) \(\Q\) None \(-1\) \(1\) \(3\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+2q^{7}+\cdots\)
6042.2.a.j \(1\) \(48.246\) \(\Q\) None \(1\) \(-1\) \(2\) \(-4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-4q^{7}+\cdots\)
6042.2.a.k \(1\) \(48.246\) \(\Q\) None \(1\) \(1\) \(1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
6042.2.a.l \(1\) \(48.246\) \(\Q\) None \(1\) \(1\) \(2\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
6042.2.a.m \(1\) \(48.246\) \(\Q\) None \(1\) \(1\) \(2\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
6042.2.a.n \(1\) \(48.246\) \(\Q\) None \(1\) \(1\) \(3\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}-q^{7}+\cdots\)
6042.2.a.o \(2\) \(48.246\) \(\Q(\sqrt{33}) \) None \(2\) \(-2\) \(-3\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
6042.2.a.p \(2\) \(48.246\) \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}-\beta q^{7}+\cdots\)
6042.2.a.q \(3\) \(48.246\) 3.3.257.1 None \(-3\) \(-3\) \(-3\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta _{2})q^{5}+q^{6}+\cdots\)
6042.2.a.r \(3\) \(48.246\) 3.3.788.1 None \(3\) \(-3\) \(2\) \(6\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(\beta _{1}+\beta _{2})q^{5}-q^{6}+\cdots\)
6042.2.a.s \(3\) \(48.246\) \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-7\) \(-7\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-2-\beta _{1})q^{5}+q^{6}+\cdots\)
6042.2.a.t \(4\) \(48.246\) 4.4.17609.1 None \(4\) \(-4\) \(6\) \(3\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(2-\beta _{3})q^{5}-q^{6}+\cdots\)
6042.2.a.u \(5\) \(48.246\) 5.5.14377697.1 None \(5\) \(-5\) \(2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{2}q^{7}+\cdots\)
6042.2.a.v \(6\) \(48.246\) 6.6.21848308.1 None \(-6\) \(6\) \(3\) \(-7\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta _{4}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6042.2.a.w \(6\) \(48.246\) 6.6.326108912.1 None \(6\) \(-6\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+\beta _{3}q^{5}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
6042.2.a.x \(6\) \(48.246\) 6.6.48689336.1 None \(6\) \(6\) \(-8\) \(-6\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1})q^{5}+q^{6}+\cdots\)
6042.2.a.y \(7\) \(48.246\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(7\) \(4\) \(-9\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
6042.2.a.z \(9\) \(48.246\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-9\) \(-1\) \(4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta _{6}q^{5}+q^{6}-\beta _{3}q^{7}+\cdots\)
6042.2.a.ba \(9\) \(48.246\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(9\) \(2\) \(10\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta _{6}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)
6042.2.a.bb \(9\) \(48.246\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-9\) \(-5\) \(-5\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta _{2})q^{5}-q^{6}+\cdots\)
6042.2.a.bc \(9\) \(48.246\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-9\) \(-3\) \(-7\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6042.2.a.bd \(11\) \(48.246\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(-11\) \(2\) \(-2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+\beta _{5}q^{7}+\cdots\)
6042.2.a.be \(12\) \(48.246\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-12\) \(-3\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+\beta _{10}q^{7}+\cdots\)
6042.2.a.bf \(12\) \(48.246\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(12\) \(-7\) \(5\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
6042.2.a.bg \(12\) \(48.246\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(12\) \(5\) \(6\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
6042.2.a.bh \(13\) \(48.246\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(13\) \(13\) \(3\) \(12\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)

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

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