Properties

Label 6534.2.a
Level $6534$
Weight $2$
Character orbit 6534.a
Rep. character $\chi_{6534}(1,\cdot)$
Character field $\Q$
Dimension $146$
Newform subspaces $76$
Sturm bound $2376$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 6534 = 2 \cdot 3^{3} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6534.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 76 \)
Sturm bound: \(2376\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\), \(17\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6534))\).

Total New Old
Modular forms 1260 146 1114
Cusp forms 1117 146 971
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.

\(2\)\(3\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(17\)
\(+\)\(+\)\(-\)\(-\)\(20\)
\(+\)\(-\)\(+\)\(-\)\(19\)
\(+\)\(-\)\(-\)\(+\)\(17\)
\(-\)\(+\)\(+\)\(-\)\(21\)
\(-\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(+\)\(15\)
\(-\)\(-\)\(-\)\(-\)\(22\)
Plus space\(+\)\(64\)
Minus space\(-\)\(82\)

Trace form

\( 146q + 146q^{4} - 6q^{7} + O(q^{10}) \) \( 146q + 146q^{4} - 6q^{7} - 10q^{10} - 16q^{13} + 146q^{16} - 4q^{19} + 132q^{25} - 6q^{28} - 10q^{31} - 16q^{34} - 20q^{37} - 10q^{40} + 28q^{43} - 4q^{46} + 168q^{49} - 16q^{52} + 4q^{58} - 32q^{61} + 146q^{64} - 12q^{67} + 10q^{70} + 30q^{73} - 4q^{76} + 24q^{79} - 20q^{82} + 24q^{85} + 96q^{91} + 44q^{94} + 90q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6534))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 11
6534.2.a.a \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}-3q^{13}+\cdots\)
6534.2.a.b \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(-3\) \(1\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
6534.2.a.c \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(-3\) \(4\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-3q^{5}+4q^{7}-q^{8}+3q^{10}+\cdots\)
6534.2.a.d \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
6534.2.a.e \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\)
6534.2.a.f \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots\)
6534.2.a.g \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-3q^{7}-q^{8}+3q^{14}+q^{16}+\cdots\)
6534.2.a.h \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(0\) \(3\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+3q^{7}-q^{8}-3q^{14}+q^{16}+\cdots\)
6534.2.a.i \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(1\) \(2\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
6534.2.a.j \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
6534.2.a.k \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
6534.2.a.l \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(2\) \(1\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
6534.2.a.m \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(3\) \(-4\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+3q^{5}-4q^{7}-q^{8}-3q^{10}+\cdots\)
6534.2.a.n \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(3\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{13}+\cdots\)
6534.2.a.o \(1\) \(52.174\) \(\Q\) None \(-1\) \(0\) \(3\) \(4\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+3q^{5}+4q^{7}-q^{8}-3q^{10}+\cdots\)
6534.2.a.p \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(-3\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-3q^{5}-4q^{7}+q^{8}-3q^{10}+\cdots\)
6534.2.a.q \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+3q^{13}+\cdots\)
6534.2.a.r \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(-3\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-3q^{5}+4q^{7}+q^{8}-3q^{10}+\cdots\)
6534.2.a.s \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(-2\) \(-1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
6534.2.a.t \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(-2\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
6534.2.a.u \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\)
6534.2.a.v \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
6534.2.a.w \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-3q^{7}+q^{8}-3q^{14}+q^{16}+\cdots\)
6534.2.a.x \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(0\) \(3\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+3q^{7}+q^{8}+3q^{14}+q^{16}+\cdots\)
6534.2.a.y \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
6534.2.a.z \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
6534.2.a.ba \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
6534.2.a.bb \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(3\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{13}+\cdots\)
6534.2.a.bc \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
6534.2.a.bd \(1\) \(52.174\) \(\Q\) None \(1\) \(0\) \(3\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+3q^{5}+4q^{7}+q^{8}+3q^{10}+\cdots\)
6534.2.a.be \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-4\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+(-1-2\beta )q^{5}-q^{7}-q^{8}+\cdots\)
6534.2.a.bf \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-2\beta q^{5}+(1-3\beta )q^{7}-q^{8}+\cdots\)
6534.2.a.bg \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(4\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}+(1+2\beta )q^{7}-q^{8}+\cdots\)
6534.2.a.bh \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(7\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-2\beta q^{5}+(3+\beta )q^{7}-q^{8}+\cdots\)
6534.2.a.bi \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-\beta q^{5}-q^{7}-q^{8}+\beta q^{10}+\cdots\)
6534.2.a.bj \(2\) \(52.174\) \(\Q(\sqrt{13}) \) None \(-2\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-\beta q^{5}+(1-2\beta )q^{7}-q^{8}+\cdots\)
6534.2.a.bk \(2\) \(52.174\) \(\Q(\sqrt{37}) \) None \(-2\) \(0\) \(-1\) \(2\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-\beta q^{5}+q^{7}-q^{8}+\beta q^{10}+\cdots\)
6534.2.a.bl \(2\) \(52.174\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+\beta q^{5}-2\beta q^{7}-q^{8}-\beta q^{10}+\cdots\)
6534.2.a.bm \(2\) \(52.174\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+2\beta q^{5}-\beta q^{7}-q^{8}-2\beta q^{10}+\cdots\)
6534.2.a.bn \(2\) \(52.174\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+\beta q^{5}+2\beta q^{7}-q^{8}-\beta q^{10}+\cdots\)
6534.2.a.bo \(2\) \(52.174\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+4\beta q^{13}+\cdots\)
6534.2.a.bp \(2\) \(52.174\) \(\Q(\sqrt{37}) \) None \(-2\) \(0\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+\beta q^{5}-q^{7}-q^{8}-\beta q^{10}+\cdots\)
6534.2.a.bq \(2\) \(52.174\) \(\Q(\sqrt{13}) \) None \(-2\) \(0\) \(1\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
6534.2.a.br \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(1\) \(2\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
6534.2.a.bs \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(2\) \(-7\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+2\beta q^{5}+(-3-\beta )q^{7}+\cdots\)
6534.2.a.bt \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(2\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{5}+(-1-2\beta )q^{7}-q^{8}+\cdots\)
6534.2.a.bu \(2\) \(52.174\) \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(2\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+(1+\beta )q^{5}-2q^{7}-q^{8}+\cdots\)
6534.2.a.bv \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(2\) \(1\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+2\beta q^{5}+(-1+3\beta )q^{7}+\cdots\)
6534.2.a.bw \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(4\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(1+2\beta )q^{5}+q^{7}-q^{8}+\cdots\)
6534.2.a.bx \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-4\) \(2\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(-1-2\beta )q^{5}+q^{7}+q^{8}+\cdots\)
6534.2.a.by \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-2\) \(-7\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-2\beta q^{5}+(-3-\beta )q^{7}+\cdots\)
6534.2.a.bz \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-2\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+(-1-2\beta )q^{7}+q^{8}+\cdots\)
6534.2.a.ca \(2\) \(52.174\) \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(-2\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+(-1+\beta )q^{5}-2q^{7}+q^{8}+\cdots\)
6534.2.a.cb \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-2\beta q^{5}+(-1+3\beta )q^{7}+\cdots\)
6534.2.a.cc \(2\) \(52.174\) \(\Q(\sqrt{37}) \) None \(2\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-\beta q^{5}-q^{7}+q^{8}-\beta q^{10}+\cdots\)
6534.2.a.cd \(2\) \(52.174\) \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
6534.2.a.ce \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-\beta q^{5}+q^{7}+q^{8}-\beta q^{10}+\cdots\)
6534.2.a.cf \(2\) \(52.174\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-4\beta q^{13}+\cdots\)
6534.2.a.cg \(2\) \(52.174\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}-2\beta q^{7}+q^{8}+\beta q^{10}+\cdots\)
6534.2.a.ch \(2\) \(52.174\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+2\beta q^{7}+q^{8}+\beta q^{10}+\cdots\)
6534.2.a.ci \(2\) \(52.174\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+2\beta q^{5}+\beta q^{7}+q^{8}+2\beta q^{10}+\cdots\)
6534.2.a.cj \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
6534.2.a.ck \(2\) \(52.174\) \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}+(1-2\beta )q^{7}+q^{8}+\cdots\)
6534.2.a.cl \(2\) \(52.174\) \(\Q(\sqrt{37}) \) None \(2\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
6534.2.a.cm \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+2\beta q^{5}+(1-3\beta )q^{7}+q^{8}+\cdots\)
6534.2.a.cn \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+q^{5}+(1+2\beta )q^{7}+q^{8}+\cdots\)
6534.2.a.co \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(7\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+2\beta q^{5}+(3+\beta )q^{7}+q^{8}+\cdots\)
6534.2.a.cp \(2\) \(52.174\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(4\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+(1+2\beta )q^{5}-q^{7}+q^{8}+\cdots\)
6534.2.a.cq \(4\) \(52.174\) 4.4.4752.1 None \(-4\) \(0\) \(0\) \(-6\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-\beta _{1}q^{5}+(-1-\beta _{2}-\beta _{3})q^{7}+\cdots\)
6534.2.a.cr \(4\) \(52.174\) 4.4.4752.1 None \(-4\) \(0\) \(0\) \(6\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+\beta _{1}q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots\)
6534.2.a.cs \(4\) \(52.174\) 4.4.4752.1 None \(4\) \(0\) \(0\) \(-6\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+\beta _{1}q^{5}+(-1-\beta _{2}-\beta _{3})q^{7}+\cdots\)
6534.2.a.ct \(4\) \(52.174\) 4.4.4752.1 None \(4\) \(0\) \(0\) \(6\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots\)
6534.2.a.cu \(6\) \(52.174\) 6.6.493090625.1 None \(-6\) \(0\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-\beta _{1}q^{5}+\beta _{3}q^{7}-q^{8}+\cdots\)
6534.2.a.cv \(6\) \(52.174\) 6.6.493090625.1 None \(-6\) \(0\) \(2\) \(1\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}-q^{8}+\cdots\)
6534.2.a.cw \(6\) \(52.174\) 6.6.493090625.1 None \(6\) \(0\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+q^{8}+\cdots\)
6534.2.a.cx \(6\) \(52.174\) 6.6.493090625.1 None \(6\) \(0\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+\beta _{1}q^{5}+\beta _{3}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6534))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6534)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(297))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(594))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2178))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3267))\)\(^{\oplus 2}\)