Properties

Label 6018.2.a
Level 6018
Weight 2
Character orbit a
Rep. character \(\chi_{6018}(1,\cdot)\)
Character field \(\Q\)
Dimension 153
Newforms 29
Sturm bound 2160
Trace bound 7

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Defining parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6018.a (trivial)
Character field: \(\Q\)
Newforms: \( 29 \)
Sturm bound: \(2160\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6018))\).

Total New Old
Modular forms 1088 153 935
Cusp forms 1073 153 920
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.

\(2\)\(3\)\(17\)\(59\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(10\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(9\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(14\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(12\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(14\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(65\)
Minus space\(-\)\(88\)

Trace form

\( 153q + q^{2} - 3q^{3} + 153q^{4} + 6q^{5} + q^{6} + q^{8} + 153q^{9} + O(q^{10}) \) \( 153q + q^{2} - 3q^{3} + 153q^{4} + 6q^{5} + q^{6} + q^{8} + 153q^{9} + 6q^{10} + 12q^{11} - 3q^{12} - 2q^{13} + 8q^{14} - 2q^{15} + 153q^{16} + q^{17} + q^{18} - 12q^{19} + 6q^{20} - 16q^{21} + 4q^{22} + 8q^{23} + q^{24} + 159q^{25} - 2q^{26} - 3q^{27} + 30q^{29} + 6q^{30} - 8q^{31} + q^{32} + 4q^{33} + q^{34} + 153q^{36} - 34q^{37} + 4q^{38} - 26q^{39} + 6q^{40} - 22q^{41} + 8q^{42} - 4q^{43} + 12q^{44} + 6q^{45} + 8q^{46} - 64q^{47} - 3q^{48} + 169q^{49} - q^{50} - 3q^{51} - 2q^{52} + 38q^{53} + q^{54} - 24q^{55} + 8q^{56} - 12q^{57} - 2q^{58} + q^{59} - 2q^{60} + 6q^{61} + 153q^{64} + 36q^{65} - 4q^{66} + 36q^{67} + q^{68} + 16q^{69} + 48q^{70} + 8q^{71} + q^{72} + 50q^{73} + 38q^{74} + 3q^{75} - 12q^{76} + 48q^{77} + 6q^{78} + 24q^{79} + 6q^{80} + 153q^{81} - 22q^{82} + 68q^{83} - 16q^{84} - 10q^{85} + 12q^{86} + 6q^{87} + 4q^{88} + 58q^{89} + 6q^{90} - 16q^{91} + 8q^{92} - 40q^{93} + 16q^{94} + 40q^{95} + q^{96} - 22q^{97} + 57q^{98} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6018))\) 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 17 59
6018.2.a.a \(1\) \(48.054\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\cdots\)
6018.2.a.b \(1\) \(48.054\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+2q^{7}+\cdots\)
6018.2.a.c \(1\) \(48.054\) \(\Q\) None \(-1\) \(-1\) \(0\) \(4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
6018.2.a.d \(1\) \(48.054\) \(\Q\) None \(-1\) \(1\) \(0\) \(5\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+5q^{7}-q^{8}+\cdots\)
6018.2.a.e \(1\) \(48.054\) \(\Q\) None \(-1\) \(1\) \(2\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
6018.2.a.f \(1\) \(48.054\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
6018.2.a.g \(1\) \(48.054\) \(\Q\) None \(1\) \(-1\) \(0\) \(3\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\)
6018.2.a.h \(1\) \(48.054\) \(\Q\) None \(1\) \(-1\) \(2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-2q^{7}+\cdots\)
6018.2.a.i \(1\) \(48.054\) \(\Q\) None \(1\) \(-1\) \(2\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
6018.2.a.j \(1\) \(48.054\) \(\Q\) None \(1\) \(1\) \(-4\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
6018.2.a.k \(1\) \(48.054\) \(\Q\) None \(1\) \(1\) \(-2\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-3q^{7}+\cdots\)
6018.2.a.l \(1\) \(48.054\) \(\Q\) None \(1\) \(1\) \(2\) \(-4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-4q^{7}+\cdots\)
6018.2.a.m \(3\) \(48.054\) 3.3.148.1 None \(-3\) \(3\) \(4\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
6018.2.a.n \(4\) \(48.054\) 4.4.2525.1 None \(4\) \(-4\) \(-3\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
6018.2.a.o \(4\) \(48.054\) 4.4.725.1 None \(4\) \(4\) \(-1\) \(-1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+\cdots\)
6018.2.a.p \(5\) \(48.054\) 5.5.1668357.1 None \(-5\) \(5\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta _{4}q^{5}-q^{6}-\beta _{1}q^{7}+\cdots\)
6018.2.a.q \(6\) \(48.054\) 6.6.5173625.1 None \(6\) \(-6\) \(-5\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
6018.2.a.r \(6\) \(48.054\) 6.6.18461324.1 None \(6\) \(6\) \(-3\) \(-7\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
6018.2.a.s \(8\) \(48.054\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-8\) \(-1\) \(6\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta _{4}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
6018.2.a.t \(8\) \(48.054\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(8\) \(-6\) \(-4\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-1-\beta _{4})q^{5}-q^{6}+\cdots\)
6018.2.a.u \(9\) \(48.054\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-9\) \(2\) \(-5\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-\beta _{6}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
6018.2.a.v \(9\) \(48.054\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-9\) \(6\) \(-11\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
6018.2.a.w \(9\) \(48.054\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(9\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{4}q^{7}+\cdots\)
6018.2.a.x \(10\) \(48.054\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-10\) \(1\) \(10\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
6018.2.a.y \(10\) \(48.054\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(10\) \(-2\) \(-6\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6018.2.a.z \(11\) \(48.054\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(11\) \(-11\) \(4\) \(3\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{2}q^{7}+\cdots\)
6018.2.a.ba \(12\) \(48.054\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(12\) \(8\) \(5\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
6018.2.a.bb \(13\) \(48.054\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(13\) \(13\) \(4\) \(11\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
6018.2.a.bc \(14\) \(48.054\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(14\) \(-14\) \(2\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{6}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6018))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(177))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(354))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1003))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2006))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3009))\)\(^{\oplus 2}\)