Properties

Label 8085.2.a
Level $8085$
Weight $2$
Character orbit 8085.a
Rep. character $\chi_{8085}(1,\cdot)$
Character field $\Q$
Dimension $272$
Newform subspaces $68$
Sturm bound $2688$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8085.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 68 \)
Sturm bound: \(2688\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(2\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8085))\).

Total New Old
Modular forms 1376 272 1104
Cusp forms 1313 272 1041
Eisenstein series 63 0 63

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

\(3\)\(5\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(19\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(17\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(14\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(20\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(20\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(20\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(12\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(15\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(21\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(14\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(24\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(21\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(122\)
Minus space\(-\)\(150\)

Trace form

\( 272 q - 4 q^{3} + 272 q^{4} + 4 q^{6} + 272 q^{9} + O(q^{10}) \) \( 272 q - 4 q^{3} + 272 q^{4} + 4 q^{6} + 272 q^{9} + 4 q^{10} - 12 q^{12} - 16 q^{13} + 4 q^{15} + 264 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{20} + 4 q^{22} + 16 q^{23} + 12 q^{24} + 272 q^{25} - 40 q^{26} - 4 q^{27} - 40 q^{32} - 4 q^{33} - 8 q^{34} + 272 q^{36} + 40 q^{37} - 16 q^{38} + 40 q^{39} + 12 q^{40} + 16 q^{41} + 32 q^{43} - 8 q^{44} - 32 q^{46} + 16 q^{47} - 28 q^{48} - 8 q^{51} - 40 q^{52} + 16 q^{53} + 4 q^{54} - 8 q^{55} + 16 q^{57} - 64 q^{58} + 12 q^{60} + 16 q^{61} + 24 q^{62} + 304 q^{64} + 8 q^{65} + 56 q^{67} - 16 q^{68} + 16 q^{69} + 16 q^{71} + 80 q^{74} - 4 q^{75} + 8 q^{76} - 8 q^{78} + 64 q^{79} + 16 q^{80} + 272 q^{81} + 24 q^{83} + 8 q^{85} - 56 q^{86} + 24 q^{87} + 12 q^{88} + 16 q^{89} + 4 q^{90} + 32 q^{92} + 40 q^{93} + 16 q^{94} - 32 q^{95} + 28 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8085))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 7 11
8085.2.a.a 8085.a 1.a $1$ $64.559$ \(\Q\) None \(-2\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots\)
8085.2.a.b 8085.a 1.a $1$ $64.559$ \(\Q\) None \(-2\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots\)
8085.2.a.c 8085.a 1.a $1$ $64.559$ \(\Q\) None \(-2\) \(-1\) \(1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{9}+\cdots\)
8085.2.a.d 8085.a 1.a $1$ $64.559$ \(\Q\) None \(-2\) \(1\) \(-1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
8085.2.a.e 8085.a 1.a $1$ $64.559$ \(\Q\) None \(-2\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots\)
8085.2.a.f 8085.a 1.a $1$ $64.559$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots\)
8085.2.a.g 8085.a 1.a $1$ $64.559$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots\)
8085.2.a.h 8085.a 1.a $1$ $64.559$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
8085.2.a.i 8085.a 1.a $1$ $64.559$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}+2q^{12}+\cdots\)
8085.2.a.j 8085.a 1.a $1$ $64.559$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}+2q^{12}+\cdots\)
8085.2.a.k 8085.a 1.a $1$ $64.559$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}+2q^{12}+\cdots\)
8085.2.a.l 8085.a 1.a $1$ $64.559$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}+q^{9}+q^{11}+2q^{12}+\cdots\)
8085.2.a.m 8085.a 1.a $1$ $64.559$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{5}+q^{9}-q^{11}+2q^{12}+\cdots\)
8085.2.a.n 8085.a 1.a $1$ $64.559$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}+q^{9}-q^{11}-2q^{12}+\cdots\)
8085.2.a.o 8085.a 1.a $1$ $64.559$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}+q^{9}-q^{11}-2q^{12}+\cdots\)
8085.2.a.p 8085.a 1.a $1$ $64.559$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}+q^{9}+q^{11}-2q^{12}+\cdots\)
8085.2.a.q 8085.a 1.a $1$ $64.559$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}+q^{9}+q^{11}-2q^{12}+\cdots\)
8085.2.a.r 8085.a 1.a $1$ $64.559$ \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots\)
8085.2.a.s 8085.a 1.a $1$ $64.559$ \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots\)
8085.2.a.t 8085.a 1.a $1$ $64.559$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots\)
8085.2.a.u 8085.a 1.a $1$ $64.559$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
8085.2.a.v 8085.a 1.a $1$ $64.559$ \(\Q\) None \(1\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots\)
8085.2.a.w 8085.a 1.a $1$ $64.559$ \(\Q\) None \(1\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots\)
8085.2.a.x 8085.a 1.a $1$ $64.559$ \(\Q\) None \(2\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
8085.2.a.y 8085.a 1.a $1$ $64.559$ \(\Q\) None \(2\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{9}+\cdots\)
8085.2.a.z 8085.a 1.a $1$ $64.559$ \(\Q\) None \(2\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{9}+\cdots\)
8085.2.a.ba 8085.a 1.a $2$ $64.559$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+q^{5}+\cdots\)
8085.2.a.bb 8085.a 1.a $2$ $64.559$ \(\Q(\sqrt{17}) \) None \(-1\) \(2\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
8085.2.a.bc 8085.a 1.a $2$ $64.559$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-2\beta q^{8}+\cdots\)
8085.2.a.bd 8085.a 1.a $2$ $64.559$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}+q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
8085.2.a.be 8085.a 1.a $2$ $64.559$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(-2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+4q^{4}-q^{5}-\beta q^{6}+2\beta q^{8}+\cdots\)
8085.2.a.bf 8085.a 1.a $2$ $64.559$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}-2\beta q^{8}+\cdots\)
8085.2.a.bg 8085.a 1.a $2$ $64.559$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}-2\beta q^{8}+\cdots\)
8085.2.a.bh 8085.a 1.a $2$ $64.559$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}+q^{5}+\cdots\)
8085.2.a.bi 8085.a 1.a $3$ $64.559$ 3.3.148.1 None \(-2\) \(-3\) \(-3\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8085.2.a.bj 8085.a 1.a $3$ $64.559$ 3.3.148.1 None \(-2\) \(3\) \(3\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8085.2.a.bk 8085.a 1.a $3$ $64.559$ 3.3.148.1 None \(-1\) \(-3\) \(-3\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
8085.2.a.bl 8085.a 1.a $3$ $64.559$ 3.3.316.1 None \(1\) \(-3\) \(-3\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.bm 8085.a 1.a $3$ $64.559$ 3.3.316.1 None \(1\) \(3\) \(-3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.bn 8085.a 1.a $4$ $64.559$ 4.4.13448.1 None \(0\) \(-4\) \(4\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.bo 8085.a 1.a $4$ $64.559$ 4.4.34196.1 None \(1\) \(-4\) \(-4\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}-q^{3}+(2-\beta _{2})q^{4}+\cdots\)
8085.2.a.bp 8085.a 1.a $4$ $64.559$ 4.4.34196.1 None \(1\) \(4\) \(4\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}+q^{3}+(2-\beta _{2})q^{4}+\cdots\)
8085.2.a.bq 8085.a 1.a $4$ $64.559$ 4.4.7232.1 None \(2\) \(4\) \(-4\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{2}-\beta _{3})q^{4}-q^{5}+\cdots\)
8085.2.a.br 8085.a 1.a $5$ $64.559$ 5.5.833376.1 None \(0\) \(-5\) \(5\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.bs 8085.a 1.a $5$ $64.559$ 5.5.833376.1 None \(0\) \(-5\) \(5\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.bt 8085.a 1.a $5$ $64.559$ 5.5.833376.1 None \(0\) \(5\) \(-5\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.bu 8085.a 1.a $5$ $64.559$ 5.5.833376.1 None \(0\) \(5\) \(-5\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.bv 8085.a 1.a $5$ $64.559$ 5.5.352076.1 None \(1\) \(-5\) \(5\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.bw 8085.a 1.a $6$ $64.559$ 6.6.2803712.1 None \(0\) \(-6\) \(6\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.bx 8085.a 1.a $6$ $64.559$ 6.6.127775712.1 None \(0\) \(-6\) \(6\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.by 8085.a 1.a $6$ $64.559$ 6.6.2803712.1 None \(0\) \(6\) \(-6\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.bz 8085.a 1.a $6$ $64.559$ 6.6.127775712.1 None \(0\) \(6\) \(-6\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.ca 8085.a 1.a $7$ $64.559$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-7\) \(7\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.cb 8085.a 1.a $7$ $64.559$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-7\) \(7\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.cc 8085.a 1.a $7$ $64.559$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(7\) \(-7\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.cd 8085.a 1.a $7$ $64.559$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(7\) \(-7\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.ce 8085.a 1.a $8$ $64.559$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-8\) \(8\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.cf 8085.a 1.a $8$ $64.559$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(-8\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.cg 8085.a 1.a $9$ $64.559$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(-9\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.ch 8085.a 1.a $9$ $64.559$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(9\) \(9\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.ci 8085.a 1.a $10$ $64.559$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(-10\) \(-10\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
8085.2.a.cj 8085.a 1.a $10$ $64.559$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(10\) \(10\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
8085.2.a.ck 8085.a 1.a $10$ $64.559$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-10\) \(-10\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.cl 8085.a 1.a $10$ $64.559$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-10\) \(10\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.cm 8085.a 1.a $10$ $64.559$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(10\) \(-10\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.cn 8085.a 1.a $10$ $64.559$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(10\) \(10\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.co 8085.a 1.a $14$ $64.559$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(4\) \(-14\) \(-14\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.cp 8085.a 1.a $14$ $64.559$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(4\) \(14\) \(14\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8085))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8085)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1617))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2695))\)\(^{\oplus 2}\)