Properties

Label 6720.2.a
Level $6720$
Weight $2$
Character orbit 6720.a
Rep. character $\chi_{6720}(1,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $80$
Sturm bound $3072$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 6720 = 2^{6} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6720.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 80 \)
Sturm bound: \(3072\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(23\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6720))\).

Total New Old
Modular forms 1584 96 1488
Cusp forms 1489 96 1393
Eisenstein series 95 0 95

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

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(40\)
Minus space\(-\)\(56\)

Trace form

\( 96q + 96q^{9} + O(q^{10}) \) \( 96q + 96q^{9} + 96q^{25} - 32q^{29} - 32q^{37} + 96q^{49} - 32q^{53} - 32q^{61} - 32q^{69} - 32q^{77} + 96q^{81} - 32q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6720))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 7
6720.2.a.a \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6720.2.a.b \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.c \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
6720.2.a.d \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6720.2.a.e \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6720.2.a.f \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
6720.2.a.g \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.h \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.i \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.j \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.k \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.l \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
6720.2.a.m \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.n \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.o \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.p \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
6720.2.a.q \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.r \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
6720.2.a.s \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}-6q^{13}-q^{15}+\cdots\)
6720.2.a.t \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.u \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
6720.2.a.v \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
6720.2.a.w \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
6720.2.a.x \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
6720.2.a.y \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6720.2.a.z \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.ba \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}-q^{15}+\cdots\)
6720.2.a.bb \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bc \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bd \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6720.2.a.be \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bf \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bg \(1\) \(53.659\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
6720.2.a.bh \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bi \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bj \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bk \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}+6q^{13}-q^{15}+\cdots\)
6720.2.a.bl \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bm \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
6720.2.a.bn \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bo \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bp \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bq \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.br \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bs \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6720.2.a.bt \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6720.2.a.bu \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
6720.2.a.bv \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
6720.2.a.bw \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bx \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
6720.2.a.by \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bz \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.ca \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
6720.2.a.cb \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6720.2.a.cc \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.cd \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.ce \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+q^{15}+\cdots\)
6720.2.a.cf \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
6720.2.a.cg \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.ch \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
6720.2.a.ci \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
6720.2.a.cj \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
6720.2.a.ck \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}-6q^{13}+q^{15}+\cdots\)
6720.2.a.cl \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.cm \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
6720.2.a.cn \(1\) \(53.659\) \(\Q\) None \(0\) \(1\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
6720.2.a.co \(2\) \(53.659\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots\)
6720.2.a.cp \(2\) \(53.659\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+\beta q^{13}+q^{15}+\cdots\)
6720.2.a.cq \(2\) \(53.659\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
6720.2.a.cr \(2\) \(53.659\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
6720.2.a.cs \(2\) \(53.659\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
6720.2.a.ct \(2\) \(53.659\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
6720.2.a.cu \(2\) \(53.659\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots\)
6720.2.a.cv \(2\) \(53.659\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}-\beta q^{13}-q^{15}+\cdots\)
6720.2.a.cw \(2\) \(53.659\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(2\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
6720.2.a.cx \(2\) \(53.659\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
6720.2.a.cy \(2\) \(53.659\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
6720.2.a.cz \(2\) \(53.659\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
6720.2.a.da \(3\) \(53.659\) 3.3.148.1 None \(0\) \(-3\) \(-3\) \(3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+(-1+\beta _{2})q^{11}+\cdots\)
6720.2.a.db \(3\) \(53.659\) 3.3.148.1 None \(0\) \(3\) \(-3\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}+(1-\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6720))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6720)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1344))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1680))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3360))\)\(^{\oplus 2}\)