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Properties

Label 8670.2.a
Level $8670$
Weight $2$
Character orbit 8670.a
Rep. character $\chi_{8670}(1,\cdot)$
Character field $\Q$
Dimension $182$
Newform subspaces $65$
Sturm bound $3672$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8670.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 65 \)
Sturm bound: \(3672\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8670))\).

Total New Old
Modular forms 1908 182 1726
Cusp forms 1765 182 1583
Eisenstein series 143 0 143

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

\(2\)\(3\)\(5\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(11\)
\(+\)\(+\)\(+\)\(-\)$-$\(12\)
\(+\)\(+\)\(-\)\(+\)$-$\(10\)
\(+\)\(+\)\(-\)\(-\)$+$\(12\)
\(+\)\(-\)\(+\)\(+\)$-$\(16\)
\(+\)\(-\)\(+\)\(-\)$+$\(7\)
\(+\)\(-\)\(-\)\(+\)$+$\(8\)
\(+\)\(-\)\(-\)\(-\)$-$\(15\)
\(-\)\(+\)\(+\)\(+\)$-$\(10\)
\(-\)\(+\)\(+\)\(-\)$+$\(12\)
\(-\)\(+\)\(-\)\(+\)$+$\(11\)
\(-\)\(+\)\(-\)\(-\)$-$\(12\)
\(-\)\(-\)\(+\)\(+\)$+$\(8\)
\(-\)\(-\)\(+\)\(-\)$-$\(15\)
\(-\)\(-\)\(-\)\(+\)$-$\(16\)
\(-\)\(-\)\(-\)\(-\)$+$\(7\)
Plus space\(+\)\(76\)
Minus space\(-\)\(106\)

Trace form

\( 182 q + 2 q^{3} + 182 q^{4} + 4 q^{7} + 182 q^{9} + O(q^{10}) \) \( 182 q + 2 q^{3} + 182 q^{4} + 4 q^{7} + 182 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 8 q^{13} - 4 q^{14} + 182 q^{16} + 4 q^{21} - 4 q^{22} - 8 q^{23} + 182 q^{25} + 12 q^{26} + 2 q^{27} + 4 q^{28} - 24 q^{29} - 2 q^{30} - 16 q^{31} - 12 q^{33} - 4 q^{35} + 182 q^{36} - 8 q^{37} + 8 q^{38} + 8 q^{39} + 2 q^{40} + 4 q^{41} - 12 q^{42} - 4 q^{44} - 16 q^{47} + 2 q^{48} + 150 q^{49} - 8 q^{52} - 16 q^{53} - 12 q^{55} - 4 q^{56} + 16 q^{57} + 4 q^{58} - 20 q^{59} + 4 q^{61} + 8 q^{62} + 4 q^{63} + 182 q^{64} + 12 q^{65} + 4 q^{66} - 8 q^{67} - 8 q^{69} - 4 q^{70} + 24 q^{71} + 44 q^{73} + 20 q^{74} + 2 q^{75} - 16 q^{77} - 4 q^{78} - 16 q^{79} + 182 q^{81} + 32 q^{82} + 16 q^{83} + 4 q^{84} + 16 q^{86} + 8 q^{87} - 4 q^{88} - 36 q^{89} + 2 q^{90} + 40 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} - 24 q^{95} + 4 q^{97} + 48 q^{98} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8670))\) 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 5 17
8670.2.a.a 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
8670.2.a.b 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
8670.2.a.c 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
8670.2.a.d 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
8670.2.a.e 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
8670.2.a.f 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(-1\) \(1\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
8670.2.a.g 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(-1\) \(1\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
8670.2.a.h 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
8670.2.a.i 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(1\) \(-1\) \(3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots\)
8670.2.a.j 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
8670.2.a.k 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
8670.2.a.l 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
8670.2.a.m 8670.a 1.a $1$ $69.230$ \(\Q\) None \(-1\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
8670.2.a.n 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
8670.2.a.o 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
8670.2.a.p 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
8670.2.a.q 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(-1\) \(1\) \(-3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots\)
8670.2.a.r 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
8670.2.a.s 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
8670.2.a.t 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(-1\) \(1\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
8670.2.a.u 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(1\) \(-1\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
8670.2.a.v 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
8670.2.a.w 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
8670.2.a.x 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(1\) \(-1\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots\)
8670.2.a.y 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(1\) \(1\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
8670.2.a.z 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
8670.2.a.ba 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
8670.2.a.bb 8670.a 1.a $1$ $69.230$ \(\Q\) None \(1\) \(1\) \(1\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
8670.2.a.bc 8670.a 1.a $2$ $69.230$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(-2\) \(4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(2+2\beta )q^{7}+\cdots\)
8670.2.a.bd 8670.a 1.a $2$ $69.230$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(-4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
8670.2.a.be 8670.a 1.a $2$ $69.230$ \(\Q(\sqrt{6}) \) None \(-2\) \(2\) \(-2\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta q^{7}+\cdots\)
8670.2.a.bf 8670.a 1.a $2$ $69.230$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(2+\beta )q^{7}+\cdots\)
8670.2.a.bg 8670.a 1.a $2$ $69.230$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(2\) \(-4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots\)
8670.2.a.bh 8670.a 1.a $2$ $69.230$ \(\Q(\sqrt{13}) \) None \(2\) \(-2\) \(-2\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
8670.2.a.bi 8670.a 1.a $2$ $69.230$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2\beta q^{7}+\cdots\)
8670.2.a.bj 8670.a 1.a $2$ $69.230$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2\beta q^{7}+\cdots\)
8670.2.a.bk 8670.a 1.a $2$ $69.230$ \(\Q(\sqrt{13}) \) None \(2\) \(2\) \(2\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
8670.2.a.bl 8670.a 1.a $3$ $69.230$ \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(-3\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta _{1}q^{7}+\cdots\)
8670.2.a.bm 8670.a 1.a $3$ $69.230$ \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(3\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.bn 8670.a 1.a $3$ $69.230$ \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(-3\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-\beta _{1}q^{7}+\cdots\)
8670.2.a.bo 8670.a 1.a $3$ $69.230$ \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(3\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.bp 8670.a 1.a $3$ $69.230$ \(\Q(\zeta_{18})^+\) None \(3\) \(-3\) \(-3\) \(6\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
8670.2.a.bq 8670.a 1.a $3$ $69.230$ \(\Q(\zeta_{18})^+\) None \(3\) \(-3\) \(3\) \(6\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
8670.2.a.br 8670.a 1.a $3$ $69.230$ \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(-3\) \(-6\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
8670.2.a.bs 8670.a 1.a $3$ $69.230$ \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(3\) \(-6\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
8670.2.a.bt 8670.a 1.a $4$ $69.230$ \(\Q(\zeta_{16})^+\) None \(-4\) \(-4\) \(4\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.bu 8670.a 1.a $4$ $69.230$ \(\Q(\zeta_{16})^+\) None \(-4\) \(-4\) \(4\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
8670.2.a.bv 8670.a 1.a $4$ $69.230$ \(\Q(\zeta_{16})^+\) None \(-4\) \(4\) \(-4\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
8670.2.a.bw 8670.a 1.a $4$ $69.230$ \(\Q(\zeta_{16})^+\) None \(-4\) \(4\) \(-4\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.bx 8670.a 1.a $4$ $69.230$ 4.4.4352.1 None \(4\) \(-4\) \(-4\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
8670.2.a.by 8670.a 1.a $4$ $69.230$ \(\Q(\zeta_{16})^+\) None \(4\) \(-4\) \(-4\) \(8\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
8670.2.a.bz 8670.a 1.a $4$ $69.230$ \(\Q(\zeta_{16})^+\) None \(4\) \(4\) \(4\) \(-8\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
8670.2.a.ca 8670.a 1.a $4$ $69.230$ 4.4.4352.1 None \(4\) \(4\) \(4\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta _{3})q^{7}+\cdots\)
8670.2.a.cb 8670.a 1.a $6$ $69.230$ 6.6.204493248.1 None \(-6\) \(-6\) \(-6\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.cc 8670.a 1.a $6$ $69.230$ 6.6.46609344.1 None \(-6\) \(-6\) \(6\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta _{5}q^{7}+\cdots\)
8670.2.a.cd 8670.a 1.a $6$ $69.230$ 6.6.46609344.1 None \(-6\) \(6\) \(-6\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{5}q^{7}+\cdots\)
8670.2.a.ce 8670.a 1.a $6$ $69.230$ 6.6.204493248.1 None \(-6\) \(6\) \(6\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.cf 8670.a 1.a $6$ $69.230$ 6.6.30652992.1 None \(6\) \(-6\) \(-6\) \(-6\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
8670.2.a.cg 8670.a 1.a $6$ $69.230$ 6.6.45769536.1 None \(6\) \(-6\) \(6\) \(-6\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
8670.2.a.ch 8670.a 1.a $6$ $69.230$ 6.6.45769536.1 None \(6\) \(6\) \(-6\) \(6\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
8670.2.a.ci 8670.a 1.a $6$ $69.230$ 6.6.30652992.1 None \(6\) \(6\) \(6\) \(6\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
8670.2.a.cj 8670.a 1.a $8$ $69.230$ 8.8.\(\cdots\).1 None \(-8\) \(-8\) \(-8\) \(-8\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
8670.2.a.ck 8670.a 1.a $8$ $69.230$ 8.8.\(\cdots\).1 None \(-8\) \(8\) \(8\) \(8\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
8670.2.a.cl 8670.a 1.a $8$ $69.230$ 8.8.\(\cdots\).1 None \(8\) \(-8\) \(8\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8670.2.a.cm 8670.a 1.a $8$ $69.230$ 8.8.\(\cdots\).1 None \(8\) \(8\) \(-8\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8670))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8670)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(867))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1445))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1734))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2890))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4335))\)\(^{\oplus 2}\)