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Properties

Label 7018.2.a
Level $7018$
Weight $2$
Character orbit 7018.a
Rep. character $\chi_{7018}(1,\cdot)$
Character field $\Q$
Dimension $253$
Newform subspaces $46$
Sturm bound $1980$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 7018 = 2 \cdot 11^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7018.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 46 \)
Sturm bound: \(1980\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7018))\).

Total New Old
Modular forms 1014 253 761
Cusp forms 967 253 714
Eisenstein series 47 0 47

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

\(2\)\(11\)\(29\)FrickeDim
\(+\)\(+\)\(+\)$+$\(34\)
\(+\)\(+\)\(-\)$-$\(31\)
\(+\)\(-\)\(+\)$-$\(28\)
\(+\)\(-\)\(-\)$+$\(33\)
\(-\)\(+\)\(+\)$-$\(35\)
\(-\)\(+\)\(-\)$+$\(26\)
\(-\)\(-\)\(+\)$+$\(28\)
\(-\)\(-\)\(-\)$-$\(38\)
Plus space\(+\)\(121\)
Minus space\(-\)\(132\)

Trace form

\( 253 q + q^{2} + 4 q^{3} + 253 q^{4} + 8 q^{5} + 2 q^{6} - 4 q^{7} + q^{8} + 255 q^{9} + O(q^{10}) \) \( 253 q + q^{2} + 4 q^{3} + 253 q^{4} + 8 q^{5} + 2 q^{6} - 4 q^{7} + q^{8} + 255 q^{9} + 2 q^{10} + 4 q^{12} - 4 q^{13} + 253 q^{16} + 14 q^{17} + 5 q^{18} - 4 q^{19} + 8 q^{20} + 4 q^{23} + 2 q^{24} + 269 q^{25} + 6 q^{26} + 4 q^{27} - 4 q^{28} + 3 q^{29} - 6 q^{30} + q^{32} + 6 q^{34} + 20 q^{35} + 255 q^{36} + 2 q^{37} + 4 q^{38} - 24 q^{39} + 2 q^{40} - 6 q^{41} + 12 q^{42} + 8 q^{43} + 66 q^{45} + 12 q^{46} + 16 q^{47} + 4 q^{48} + 269 q^{49} + 23 q^{50} - 4 q^{51} - 4 q^{52} + 32 q^{53} + 26 q^{54} - q^{58} + 12 q^{59} - 14 q^{61} + 2 q^{62} - 32 q^{63} + 253 q^{64} + 6 q^{65} + 24 q^{67} + 14 q^{68} - 4 q^{69} + 16 q^{70} + 16 q^{71} + 5 q^{72} + 2 q^{73} + 2 q^{74} + 24 q^{75} - 4 q^{76} - 2 q^{78} - 8 q^{79} + 8 q^{80} + 269 q^{81} + 38 q^{82} - 12 q^{83} + 32 q^{85} + 38 q^{86} + 42 q^{89} - 10 q^{90} - 116 q^{91} + 4 q^{92} - 154 q^{93} + 10 q^{94} - 16 q^{95} + 2 q^{96} - 94 q^{97} - 7 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7018))\) 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 11 29
7018.2.a.a 7018.a 1.a $1$ $56.039$ \(\Q\) None \(-1\) \(-1\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
7018.2.a.b 7018.a 1.a $1$ $56.039$ \(\Q\) None \(-1\) \(0\) \(-2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}-3q^{9}+\cdots\)
7018.2.a.c 7018.a 1.a $1$ $56.039$ \(\Q\) None \(1\) \(-3\) \(-3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-3q^{5}-3q^{6}+2q^{7}+\cdots\)
7018.2.a.d 7018.a 1.a $1$ $56.039$ \(\Q\) None \(1\) \(0\) \(-2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}-4q^{7}+q^{8}-3q^{9}+\cdots\)
7018.2.a.e 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{13}) \) None \(-2\) \(-3\) \(-4\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta )q^{3}+q^{4}-2q^{5}+(1+\cdots)q^{6}+\cdots\)
7018.2.a.f 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{5}) \) None \(-2\) \(-3\) \(-2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta )q^{3}+q^{4}-2\beta q^{5}+\cdots\)
7018.2.a.g 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{5}) \) None \(-2\) \(-3\) \(-2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-2+2\beta )q^{5}+\cdots\)
7018.2.a.h 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(-4\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+(-1-2\beta )q^{5}+\cdots\)
7018.2.a.i 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(2\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+2\beta q^{5}+\beta q^{6}+\cdots\)
7018.2.a.j 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{5}) \) None \(-2\) \(3\) \(-6\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}-3q^{5}+(-1+\cdots)q^{6}+\cdots\)
7018.2.a.k 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}-2\beta q^{5}+\cdots\)
7018.2.a.l 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
7018.2.a.m 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(-4\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+(-1-2\beta )q^{5}+\cdots\)
7018.2.a.n 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(2\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+2\beta q^{5}-\beta q^{6}+\cdots\)
7018.2.a.o 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+(2-2\beta )q^{5}+\beta q^{6}+\cdots\)
7018.2.a.p 7018.a 1.a $2$ $56.039$ \(\Q(\sqrt{5}) \) None \(2\) \(3\) \(-6\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}-3q^{5}+(1+\beta )q^{6}+\cdots\)
7018.2.a.q 7018.a 1.a $3$ $56.039$ 3.3.169.1 None \(-3\) \(-5\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-2+\beta _{1})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
7018.2.a.r 7018.a 1.a $3$ $56.039$ 3.3.321.1 None \(-3\) \(-1\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
7018.2.a.s 7018.a 1.a $3$ $56.039$ 3.3.169.1 None \(3\) \(-5\) \(2\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-2+\beta _{1})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
7018.2.a.t 7018.a 1.a $3$ $56.039$ 3.3.321.1 None \(3\) \(-1\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
7018.2.a.u 7018.a 1.a $4$ $56.039$ 4.4.4752.1 None \(-4\) \(2\) \(-6\) \(10\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{2}-\beta _{3})q^{5}+\cdots\)
7018.2.a.v 7018.a 1.a $4$ $56.039$ 4.4.35312.1 None \(-4\) \(2\) \(0\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{2}q^{5}+(-1+\cdots)q^{6}+\cdots\)
7018.2.a.w 7018.a 1.a $4$ $56.039$ 4.4.5744.1 None \(-4\) \(4\) \(2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{3})q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
7018.2.a.x 7018.a 1.a $4$ $56.039$ 4.4.4752.1 None \(4\) \(2\) \(-6\) \(-10\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{2}-\beta _{3})q^{5}+\cdots\)
7018.2.a.y 7018.a 1.a $4$ $56.039$ 4.4.61504.1 None \(4\) \(2\) \(-4\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
7018.2.a.z 7018.a 1.a $5$ $56.039$ 5.5.4557264.1 None \(5\) \(4\) \(4\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{3})q^{5}+\cdots\)
7018.2.a.ba 7018.a 1.a $6$ $56.039$ 6.6.19452096.1 None \(-6\) \(-6\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{4}q^{5}+\cdots\)
7018.2.a.bb 7018.a 1.a $6$ $56.039$ 6.6.370008144.1 None \(-6\) \(-3\) \(-4\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
7018.2.a.bc 7018.a 1.a $6$ $56.039$ 6.6.233763408.1 None \(-6\) \(3\) \(8\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{3})q^{3}+q^{4}+(1+\beta _{1})q^{5}+\cdots\)
7018.2.a.bd 7018.a 1.a $6$ $56.039$ 6.6.527151533.1 None \(-6\) \(4\) \(6\) \(-5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots\)
7018.2.a.be 7018.a 1.a $6$ $56.039$ 6.6.171485053.1 None \(-6\) \(4\) \(6\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{3})q^{3}+q^{4}+(1-\beta _{5})q^{5}+\cdots\)
7018.2.a.bf 7018.a 1.a $6$ $56.039$ 6.6.19452096.1 None \(6\) \(-6\) \(-2\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{4}q^{5}+\cdots\)
7018.2.a.bg 7018.a 1.a $6$ $56.039$ 6.6.370008144.1 None \(6\) \(-3\) \(-4\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
7018.2.a.bh 7018.a 1.a $6$ $56.039$ 6.6.233763408.1 None \(6\) \(3\) \(8\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{3})q^{3}+q^{4}+(1+\beta _{1})q^{5}+\cdots\)
7018.2.a.bi 7018.a 1.a $6$ $56.039$ 6.6.171485053.1 None \(6\) \(4\) \(6\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{3})q^{3}+q^{4}+(1-\beta _{5})q^{5}+\cdots\)
7018.2.a.bj 7018.a 1.a $6$ $56.039$ 6.6.527151533.1 None \(6\) \(4\) \(6\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots\)
7018.2.a.bk 7018.a 1.a $8$ $56.039$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(2\) \(-5\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
7018.2.a.bl 7018.a 1.a $8$ $56.039$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(2\) \(-5\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
7018.2.a.bm 7018.a 1.a $10$ $56.039$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-1\) \(-5\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{9})q^{5}+\cdots\)
7018.2.a.bn 7018.a 1.a $10$ $56.039$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-1\) \(-5\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{9})q^{5}+\cdots\)
7018.2.a.bo 7018.a 1.a $12$ $56.039$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(8\) \(12\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{9})q^{5}+\cdots\)
7018.2.a.bp 7018.a 1.a $12$ $56.039$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(8\) \(12\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{9})q^{5}+\cdots\)
7018.2.a.bq 7018.a 1.a $16$ $56.039$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(-1\) \(1\) \(-10\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{14}q^{5}+\beta _{1}q^{6}+\cdots\)
7018.2.a.br 7018.a 1.a $16$ $56.039$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(-1\) \(1\) \(10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{14}q^{5}-\beta _{1}q^{6}+\cdots\)
7018.2.a.bs 7018.a 1.a $18$ $56.039$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-18\) \(-2\) \(5\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots\)
7018.2.a.bt 7018.a 1.a $18$ $56.039$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(18\) \(-2\) \(5\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7018))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(319))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(638))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3509))\)\(^{\oplus 2}\)