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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 7 11
8085.2.a.a \(1\) \(64.559\) \(\Q\) None \(-2\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots\)
8085.2.a.b \(1\) \(64.559\) \(\Q\) None \(-2\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots\)
8085.2.a.c \(1\) \(64.559\) \(\Q\) None \(-2\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{9}+\cdots\)
8085.2.a.d \(1\) \(64.559\) \(\Q\) None \(-2\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
8085.2.a.e \(1\) \(64.559\) \(\Q\) None \(-2\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots\)
8085.2.a.f \(1\) \(64.559\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots\)
8085.2.a.g \(1\) \(64.559\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots\)
8085.2.a.h \(1\) \(64.559\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
8085.2.a.i \(1\) \(64.559\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}+2q^{12}+\cdots\)
8085.2.a.j \(1\) \(64.559\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}+2q^{12}+\cdots\)
8085.2.a.k \(1\) \(64.559\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}+2q^{12}+\cdots\)
8085.2.a.l \(1\) \(64.559\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{4}-q^{5}+q^{9}+q^{11}+2q^{12}+\cdots\)
8085.2.a.m \(1\) \(64.559\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{3}-2q^{4}+q^{5}+q^{9}-q^{11}+2q^{12}+\cdots\)
8085.2.a.n \(1\) \(64.559\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-2q^{4}+q^{5}+q^{9}-q^{11}-2q^{12}+\cdots\)
8085.2.a.o \(1\) \(64.559\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-2q^{4}+q^{5}+q^{9}-q^{11}-2q^{12}+\cdots\)
8085.2.a.p \(1\) \(64.559\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}+q^{5}+q^{9}+q^{11}-2q^{12}+\cdots\)
8085.2.a.q \(1\) \(64.559\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}+q^{5}+q^{9}+q^{11}-2q^{12}+\cdots\)
8085.2.a.r \(1\) \(64.559\) \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots\)
8085.2.a.s \(1\) \(64.559\) \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots\)
8085.2.a.t \(1\) \(64.559\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots\)
8085.2.a.u \(1\) \(64.559\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
8085.2.a.v \(1\) \(64.559\) \(\Q\) None \(1\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots\)
8085.2.a.w \(1\) \(64.559\) \(\Q\) None \(1\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots\)
8085.2.a.x \(1\) \(64.559\) \(\Q\) None \(2\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
8085.2.a.y \(1\) \(64.559\) \(\Q\) None \(2\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{9}+\cdots\)
8085.2.a.z \(1\) \(64.559\) \(\Q\) None \(2\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{9}+\cdots\)
8085.2.a.ba \(2\) \(64.559\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+q^{5}+\cdots\)
8085.2.a.bb \(2\) \(64.559\) \(\Q(\sqrt{17}) \) None \(-1\) \(2\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
8085.2.a.bc \(2\) \(64.559\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-2\beta q^{8}+\cdots\)
8085.2.a.bd \(2\) \(64.559\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q+\beta q^{2}-q^{3}+q^{4}+q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
8085.2.a.be \(2\) \(64.559\) \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q+\beta q^{2}-q^{3}+4q^{4}-q^{5}-\beta q^{6}+2\beta q^{8}+\cdots\)
8085.2.a.bf \(2\) \(64.559\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}-2\beta q^{8}+\cdots\)
8085.2.a.bg \(2\) \(64.559\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}-2\beta q^{8}+\cdots\)
8085.2.a.bh \(2\) \(64.559\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}+q^{5}+\cdots\)
8085.2.a.bi \(3\) \(64.559\) 3.3.148.1 None \(-2\) \(-3\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8085.2.a.bj \(3\) \(64.559\) 3.3.148.1 None \(-2\) \(3\) \(3\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8085.2.a.bk \(3\) \(64.559\) 3.3.148.1 None \(-1\) \(-3\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
8085.2.a.bl \(3\) \(64.559\) 3.3.316.1 None \(1\) \(-3\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.bm \(3\) \(64.559\) 3.3.316.1 None \(1\) \(3\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.bn \(4\) \(64.559\) 4.4.13448.1 None \(0\) \(-4\) \(4\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.bo \(4\) \(64.559\) 4.4.34196.1 None \(1\) \(-4\) \(-4\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{2}-q^{3}+(2-\beta _{2})q^{4}+\cdots\)
8085.2.a.bp \(4\) \(64.559\) 4.4.34196.1 None \(1\) \(4\) \(4\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{2}+q^{3}+(2-\beta _{2})q^{4}+\cdots\)
8085.2.a.bq \(4\) \(64.559\) 4.4.7232.1 None \(2\) \(4\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{2}-\beta _{3})q^{4}-q^{5}+\cdots\)
8085.2.a.br \(5\) \(64.559\) 5.5.833376.1 None \(0\) \(-5\) \(5\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.bs \(5\) \(64.559\) 5.5.833376.1 None \(0\) \(-5\) \(5\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.bt \(5\) \(64.559\) 5.5.833376.1 None \(0\) \(5\) \(-5\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.bu \(5\) \(64.559\) 5.5.833376.1 None \(0\) \(5\) \(-5\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.bv \(5\) \(64.559\) 5.5.352076.1 None \(1\) \(-5\) \(5\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.bw \(6\) \(64.559\) 6.6.2803712.1 None \(0\) \(-6\) \(6\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.bx \(6\) \(64.559\) 6.6.127775712.1 None \(0\) \(-6\) \(6\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.by \(6\) \(64.559\) 6.6.2803712.1 None \(0\) \(6\) \(-6\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.bz \(6\) \(64.559\) 6.6.127775712.1 None \(0\) \(6\) \(-6\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.ca \(7\) \(64.559\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-7\) \(7\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.cb \(7\) \(64.559\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-7\) \(7\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.cc \(7\) \(64.559\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(7\) \(-7\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.cd \(7\) \(64.559\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(7\) \(-7\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.ce \(8\) \(64.559\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-8\) \(8\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.cf \(8\) \(64.559\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(-8\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.cg \(9\) \(64.559\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(-9\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.ch \(9\) \(64.559\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(9\) \(9\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.ci \(10\) \(64.559\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(-10\) \(-10\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
8085.2.a.cj \(10\) \(64.559\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(10\) \(10\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
8085.2.a.ck \(10\) \(64.559\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-10\) \(-10\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.cl \(10\) \(64.559\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-10\) \(10\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.cm \(10\) \(64.559\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(10\) \(-10\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
8085.2.a.cn \(10\) \(64.559\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(10\) \(10\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.co \(14\) \(64.559\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(4\) \(-14\) \(-14\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
8085.2.a.cp \(14\) \(64.559\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(4\) \(14\) \(14\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

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

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