Properties

Label 8281.2.a
Level $8281$
Weight $2$
Character orbit 8281.a
Rep. character $\chi_{8281}(1,\cdot)$
Character field $\Q$
Dimension $502$
Newform subspaces $78$
Sturm bound $1698$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 8281 = 7^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8281.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 78 \)
Sturm bound: \(1698\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(2\), \(3\), \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8281))\).

Total New Old
Modular forms 904 557 347
Cusp forms 793 502 291
Eisenstein series 111 55 56

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

\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(118\)
\(+\)\(-\)\(-\)\(130\)
\(-\)\(+\)\(-\)\(131\)
\(-\)\(-\)\(+\)\(123\)
Plus space\(+\)\(241\)
Minus space\(-\)\(261\)

Trace form

\( 502q - 4q^{3} + 472q^{4} + 2q^{5} + 12q^{8} + 442q^{9} + O(q^{10}) \) \( 502q - 4q^{3} + 472q^{4} + 2q^{5} + 12q^{8} + 442q^{9} + 6q^{10} - 4q^{11} - 4q^{12} - 4q^{15} + 416q^{16} + 4q^{18} - 12q^{19} - 2q^{20} + 14q^{22} + 6q^{23} - 4q^{24} + 404q^{25} + 2q^{27} + 20q^{29} + 58q^{30} - 4q^{31} + 44q^{32} - 4q^{33} + 2q^{34} + 354q^{36} + 16q^{37} - 20q^{38} + 14q^{40} + 2q^{41} + 22q^{43} + 28q^{44} + 22q^{45} + 8q^{46} + 8q^{47} + 46q^{48} + 40q^{50} + 6q^{51} + 16q^{53} + 48q^{54} + 16q^{55} + 16q^{57} + 40q^{58} + 16q^{59} - 24q^{61} - 10q^{62} + 318q^{64} + 26q^{66} + 90q^{68} - 16q^{69} - 28q^{71} + 40q^{72} - 22q^{73} + 70q^{74} - 54q^{75} + 16q^{76} + 34q^{79} - 38q^{80} + 246q^{81} + 52q^{82} + 24q^{83} + 24q^{85} - 52q^{86} + 16q^{87} + 42q^{88} + 26q^{89} + 28q^{90} - 140q^{92} + 28q^{93} - 2q^{94} + 22q^{95} - 4q^{96} - 6q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8281))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 13
8281.2.a.a \(1\) \(66.124\) \(\Q\) None \(-2\) \(-2\) \(-1\) \(0\) \(-\) \(-\) \(q-2q^{2}-2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
8281.2.a.b \(1\) \(66.124\) \(\Q\) None \(-2\) \(2\) \(1\) \(0\) \(-\) \(-\) \(q-2q^{2}+2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
8281.2.a.c \(1\) \(66.124\) \(\Q\) None \(-1\) \(-3\) \(-3\) \(0\) \(+\) \(+\) \(q-q^{2}-3q^{3}-q^{4}-3q^{5}+3q^{6}+3q^{8}+\cdots\)
8281.2.a.d \(1\) \(66.124\) \(\Q\) \(\Q(\sqrt{-7}) \) \(-1\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q-q^{2}-q^{4}+3q^{8}-3q^{9}-4q^{11}+\cdots\)
8281.2.a.e \(1\) \(66.124\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots\)
8281.2.a.f \(1\) \(66.124\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots\)
8281.2.a.g \(1\) \(66.124\) \(\Q\) None \(-1\) \(3\) \(3\) \(0\) \(-\) \(+\) \(q-q^{2}+3q^{3}-q^{4}+3q^{5}-3q^{6}+3q^{8}+\cdots\)
8281.2.a.h \(1\) \(66.124\) \(\Q\) None \(0\) \(2\) \(-3\) \(0\) \(-\) \(+\) \(q+2q^{3}-2q^{4}-3q^{5}+q^{9}-4q^{12}+\cdots\)
8281.2.a.i \(1\) \(66.124\) \(\Q\) None \(1\) \(-3\) \(3\) \(0\) \(+\) \(+\) \(q+q^{2}-3q^{3}-q^{4}+3q^{5}-3q^{6}-3q^{8}+\cdots\)
8281.2.a.j \(1\) \(66.124\) \(\Q\) None \(1\) \(3\) \(-3\) \(0\) \(-\) \(+\) \(q+q^{2}+3q^{3}-q^{4}-3q^{5}+3q^{6}-3q^{8}+\cdots\)
8281.2.a.k \(1\) \(66.124\) \(\Q\) None \(2\) \(-2\) \(1\) \(0\) \(-\) \(-\) \(q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
8281.2.a.l \(1\) \(66.124\) \(\Q\) None \(2\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(q+2q^{2}+2q^{4}-3q^{5}-3q^{9}-6q^{10}+\cdots\)
8281.2.a.m \(1\) \(66.124\) \(\Q\) None \(2\) \(2\) \(-1\) \(0\) \(-\) \(-\) \(q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
8281.2.a.n \(2\) \(66.124\) \(\Q(\sqrt{5}) \) None \(-3\) \(3\) \(3\) \(0\) \(-\) \(+\) \(q+(-1-\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+\cdots\)
8281.2.a.o \(2\) \(66.124\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
8281.2.a.p \(2\) \(66.124\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(-\) \(+\) \(q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
8281.2.a.q \(2\) \(66.124\) \(\Q(\sqrt{3}) \) None \(0\) \(-4\) \(0\) \(0\) \(-\) \(-\) \(q+\beta q^{2}-2q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\)
8281.2.a.r \(2\) \(66.124\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
8281.2.a.s \(2\) \(66.124\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
8281.2.a.t \(2\) \(66.124\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
8281.2.a.u \(2\) \(66.124\) \(\Q(\sqrt{13}) \) \(\Q(\sqrt{-91}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q-2q^{4}-\beta q^{5}-3q^{9}+4q^{16}-\beta q^{19}+\cdots\)
8281.2.a.v \(2\) \(66.124\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(6\) \(0\) \(-\) \(+\) \(q+\beta q^{2}-\beta q^{3}+(3-\beta )q^{5}-2q^{6}-2\beta q^{8}+\cdots\)
8281.2.a.w \(2\) \(66.124\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{5}+\beta q^{6}-\beta q^{8}+\cdots\)
8281.2.a.x \(2\) \(66.124\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots\)
8281.2.a.y \(2\) \(66.124\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(+\) \(q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
8281.2.a.z \(2\) \(66.124\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+(1+\cdots)q^{5}+\cdots\)
8281.2.a.ba \(2\) \(66.124\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+(1+\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
8281.2.a.bb \(2\) \(66.124\) \(\Q(\sqrt{5}) \) None \(3\) \(3\) \(-3\) \(0\) \(-\) \(+\) \(q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+(-1+\cdots)q^{5}+\cdots\)
8281.2.a.bc \(3\) \(66.124\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(-4\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bd \(3\) \(66.124\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(-3\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots\)
8281.2.a.be \(3\) \(66.124\) 3.3.148.1 None \(-2\) \(0\) \(3\) \(0\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bf \(3\) \(66.124\) \(\Q(\zeta_{14})^+\) None \(-2\) \(2\) \(4\) \(0\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bg \(3\) \(66.124\) 3.3.316.1 None \(-1\) \(2\) \(2\) \(0\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
8281.2.a.bh \(3\) \(66.124\) 3.3.404.1 None \(2\) \(-4\) \(5\) \(0\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bi \(3\) \(66.124\) 3.3.148.1 None \(2\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bj \(3\) \(66.124\) \(\Q(\zeta_{14})^+\) None \(2\) \(2\) \(-4\) \(0\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bk \(3\) \(66.124\) 3.3.404.1 None \(2\) \(4\) \(-5\) \(0\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.bl \(3\) \(66.124\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(3\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}+(5+\cdots)q^{8}+\cdots\)
8281.2.a.bm \(3\) \(66.124\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) \(4\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(4+\cdots)q^{8}+\cdots\)
8281.2.a.bn \(4\) \(66.124\) \(\Q(\sqrt{2}, \sqrt{23})\) None \(-4\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q-q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
8281.2.a.bo \(4\) \(66.124\) 4.4.105456.1 None \(-2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)
8281.2.a.bp \(4\) \(66.124\) 4.4.27004.1 None \(-1\) \(-1\) \(7\) \(0\) \(-\) \(+\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bq \(4\) \(66.124\) \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(-\) \(q+\beta _{3}q^{2}+(-1-\beta _{2})q^{3}-\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
8281.2.a.br \(4\) \(66.124\) \(\Q(\sqrt{3}, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q-\beta _{2}q^{2}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{8}-3q^{9}+\cdots\)
8281.2.a.bs \(4\) \(66.124\) \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}-\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots\)
8281.2.a.bt \(4\) \(66.124\) 4.4.27004.1 None \(1\) \(-1\) \(-7\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
8281.2.a.bu \(4\) \(66.124\) 4.4.105456.1 None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
8281.2.a.bv \(4\) \(66.124\) \(\Q(\sqrt{2}, \sqrt{23})\) None \(4\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+q^{2}+\beta _{2}q^{3}-q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
8281.2.a.bw \(5\) \(66.124\) 5.5.746052.1 None \(-4\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.bx \(5\) \(66.124\) 5.5.746052.1 None \(-4\) \(0\) \(2\) \(0\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.by \(6\) \(66.124\) 6.6.7674048.1 None \(-4\) \(0\) \(6\) \(0\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
8281.2.a.bz \(6\) \(66.124\) 6.6.6995813.1 None \(-2\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(q+(-\beta _{1}+\beta _{4})q^{2}+\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.ca \(6\) \(66.124\) 6.6.6995813.1 None \(-2\) \(1\) \(1\) \(0\) \(-\) \(+\) \(q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.cb \(6\) \(66.124\) 6.6.1279733.1 None \(-2\) \(4\) \(2\) \(0\) \(-\) \(-\) \(q+(-1+\beta _{2}+\beta _{4})q^{2}+(\beta _{1}-\beta _{3})q^{3}+\cdots\)
8281.2.a.cc \(6\) \(66.124\) 6.6.4507648.1 None \(0\) \(-8\) \(6\) \(0\) \(+\) \(+\) \(q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.cd \(6\) \(66.124\) 6.6.4507648.1 None \(0\) \(8\) \(-6\) \(0\) \(+\) \(+\) \(q+\beta _{2}q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
8281.2.a.ce \(6\) \(66.124\) 6.6.6995813.1 None \(2\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(q+(\beta _{1}-\beta _{4})q^{2}+\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.cf \(6\) \(66.124\) 6.6.6995813.1 None \(2\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(q+(\beta _{1}-\beta _{4})q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots\)
8281.2.a.cg \(6\) \(66.124\) 6.6.1279733.1 None \(2\) \(4\) \(-2\) \(0\) \(-\) \(+\) \(q+(1-\beta _{2}-\beta _{4})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
8281.2.a.ch \(6\) \(66.124\) 6.6.7674048.1 None \(4\) \(0\) \(-6\) \(0\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
8281.2.a.ci \(8\) \(66.124\) 8.8.8446345216.1 None \(-4\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+(-1-\beta _{5})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1+\cdots)q^{4}+\cdots\)
8281.2.a.cj \(8\) \(66.124\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
8281.2.a.ck \(8\) \(66.124\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
8281.2.a.cl \(8\) \(66.124\) 8.8.8446345216.1 None \(4\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+(1+\beta _{5})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
8281.2.a.cm \(12\) \(66.124\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
8281.2.a.cn \(12\) \(66.124\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(-8\) \(-4\) \(0\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
8281.2.a.co \(12\) \(66.124\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-6\) \(0\) \(0\) \(-\) \(-\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1-\beta _{8}+\beta _{9})q^{4}+\cdots\)
8281.2.a.cp \(12\) \(66.124\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(6\) \(0\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1-\beta _{8}+\beta _{9})q^{4}+\cdots\)
8281.2.a.cq \(12\) \(66.124\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(-8\) \(4\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
8281.2.a.cr \(12\) \(66.124\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
8281.2.a.cs \(16\) \(66.124\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q+\beta _{7}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
8281.2.a.ct \(24\) \(66.124\) None \(-1\) \(0\) \(-13\) \(0\) \(-\) \(-\)
8281.2.a.cu \(24\) \(66.124\) None \(-1\) \(0\) \(13\) \(0\) \(+\) \(-\)
8281.2.a.cv \(24\) \(66.124\) None \(1\) \(0\) \(-13\) \(0\) \(+\) \(+\)
8281.2.a.cw \(24\) \(66.124\) None \(1\) \(0\) \(13\) \(0\) \(-\) \(+\)
8281.2.a.cx \(32\) \(66.124\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\)
8281.2.a.cy \(36\) \(66.124\) None \(-14\) \(0\) \(0\) \(0\) \(+\) \(+\)
8281.2.a.cz \(36\) \(66.124\) None \(14\) \(0\) \(0\) \(0\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8281))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8281)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 2}\)