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Properties

Label 6018.2.a
Level $6018$
Weight $2$
Character orbit 6018.a
Rep. character $\chi_{6018}(1,\cdot)$
Character field $\Q$
Dimension $153$
Newform subspaces $29$
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: \(\Q\)
Newform subspaces: \( 29 \)
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

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

Display 100 coefficients 10 coefficients

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

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

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