Properties

Label 7056.2.a
Level $7056$
Weight $2$
Character orbit 7056.a
Rep. character $\chi_{7056}(1,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $77$
Sturm bound $2688$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7056.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 77 \)
Sturm bound: \(2688\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7056))\).

Total New Old
Modular forms 1440 105 1335
Cusp forms 1249 100 1149
Eisenstein series 191 5 186

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

\(2\)\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(-\)\(-\)\(+\)\(15\)
\(-\)\(+\)\(+\)\(-\)\(12\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(45\)
Minus space\(-\)\(55\)

Trace form

\( 100q + O(q^{10}) \) \( 100q + 2q^{11} + 2q^{13} - 4q^{17} - 4q^{19} + 2q^{23} + 94q^{25} + 14q^{29} - 4q^{31} + 6q^{37} - 4q^{41} - 4q^{43} - 28q^{59} + 6q^{61} - 8q^{65} - 2q^{67} - 40q^{71} + 2q^{73} - 22q^{79} + 12q^{83} + 18q^{85} - 12q^{89} - 34q^{95} + 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7056))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7
7056.2.a.a \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(q-4q^{5}-4q^{11}+4q^{13}-4q^{19}+11q^{25}+\cdots\)
7056.2.a.b \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(q-4q^{5}-3q^{13}+4q^{17}-7q^{19}+4q^{23}+\cdots\)
7056.2.a.c \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{5}-2q^{17}-2q^{19}+8q^{23}+11q^{25}+\cdots\)
7056.2.a.d \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-4\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{5}+3q^{13}+4q^{17}+7q^{19}-4q^{23}+\cdots\)
7056.2.a.e \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(q-3q^{5}-3q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\)
7056.2.a.f \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q-3q^{5}-3q^{11}+2q^{13}-3q^{17}+q^{19}+\cdots\)
7056.2.a.g \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q-3q^{5}+3q^{11}-4q^{13}+4q^{19}+4q^{25}+\cdots\)
7056.2.a.h \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{5}+3q^{11}-2q^{13}-6q^{17}+2q^{19}+\cdots\)
7056.2.a.i \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{5}-6q^{11}-3q^{13}-4q^{17}+5q^{19}+\cdots\)
7056.2.a.j \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q-2q^{5}-6q^{11}+6q^{13}+2q^{17}+4q^{19}+\cdots\)
7056.2.a.k \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{5}-4q^{11}-6q^{13}+2q^{17}-4q^{19}+\cdots\)
7056.2.a.l \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q-2q^{5}-2q^{11}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
7056.2.a.m \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{5}-2q^{11}-q^{13}+q^{19}-q^{25}+\cdots\)
7056.2.a.n \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{5}+2q^{11}-4q^{13}-6q^{17}-8q^{19}+\cdots\)
7056.2.a.o \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{5}+2q^{11}+3q^{13}+8q^{17}-q^{19}+\cdots\)
7056.2.a.p \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{5}+4q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
7056.2.a.q \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{5}+4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots\)
7056.2.a.r \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{5}-5q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots\)
7056.2.a.s \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{5}-q^{11}-2q^{13}+3q^{17}+5q^{19}+\cdots\)
7056.2.a.t \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{5}+3q^{11}-4q^{13}-4q^{19}+8q^{23}+\cdots\)
7056.2.a.u \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{5}+3q^{11}+6q^{13}-5q^{17}+q^{19}+\cdots\)
7056.2.a.v \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q-q^{5}+5q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots\)
7056.2.a.w \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(q-q^{5}+5q^{11}+4q^{17}-8q^{19}-4q^{23}+\cdots\)
7056.2.a.x \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-6q^{11}-2q^{13}-4q^{19}-6q^{23}+\cdots\)
7056.2.a.y \(1\) \(56.342\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-7q^{13}+7q^{19}-5q^{25}+7q^{31}+\cdots\)
7056.2.a.z \(1\) \(56.342\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-5q^{13}-q^{19}-5q^{25}+11q^{31}+\cdots\)
7056.2.a.ba \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{13}+4q^{17}-4q^{19}+4q^{23}+\cdots\)
7056.2.a.bb \(1\) \(56.342\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{13}+8q^{19}-5q^{25}-4q^{31}+\cdots\)
7056.2.a.bc \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+4q^{13}-4q^{17}+4q^{19}+4q^{23}+\cdots\)
7056.2.a.bd \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots\)
7056.2.a.be \(1\) \(56.342\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+5q^{13}+q^{19}-5q^{25}-11q^{31}+\cdots\)
7056.2.a.bf \(1\) \(56.342\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+7q^{13}-7q^{19}-5q^{25}-7q^{31}+\cdots\)
7056.2.a.bg \(1\) \(56.342\) \(\Q\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{11}+8q^{23}-5q^{25}-2q^{29}+\cdots\)
7056.2.a.bh \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(+\) \(-\) \(q+q^{5}-5q^{11}-2q^{13}-6q^{17}+2q^{19}+\cdots\)
7056.2.a.bi \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q+q^{5}-q^{11}+2q^{13}-3q^{17}-5q^{19}+\cdots\)
7056.2.a.bj \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q+q^{5}+3q^{11}-6q^{13}+5q^{17}-q^{19}+\cdots\)
7056.2.a.bk \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q+q^{5}+3q^{11}+4q^{13}+4q^{19}+8q^{23}+\cdots\)
7056.2.a.bl \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{5}+5q^{11}-4q^{17}+8q^{19}-4q^{23}+\cdots\)
7056.2.a.bm \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(+\) \(+\) \(q+q^{5}+5q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\)
7056.2.a.bn \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{5}-6q^{11}+3q^{13}+4q^{17}-5q^{19}+\cdots\)
7056.2.a.bo \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{5}-4q^{11}-2q^{13}-6q^{17}+8q^{19}+\cdots\)
7056.2.a.bp \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{5}-2q^{11}+q^{13}-q^{19}-q^{25}+\cdots\)
7056.2.a.bq \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{5}-6q^{13}-2q^{17}+4q^{19}-4q^{23}+\cdots\)
7056.2.a.br \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{5}+2q^{13}+6q^{17}-4q^{19}-4q^{23}+\cdots\)
7056.2.a.bs \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{5}+2q^{11}-3q^{13}-8q^{17}+q^{19}+\cdots\)
7056.2.a.bt \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q+2q^{5}+2q^{11}-2q^{13}+6q^{17}-4q^{19}+\cdots\)
7056.2.a.bu \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{5}+2q^{11}+4q^{13}+6q^{17}+8q^{19}+\cdots\)
7056.2.a.bv \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q+2q^{5}+6q^{11}+6q^{13}-2q^{17}+4q^{19}+\cdots\)
7056.2.a.bw \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{5}-3q^{11}-2q^{13}+3q^{17}-q^{19}+\cdots\)
7056.2.a.bx \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(+\) \(-\) \(q+3q^{5}-3q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots\)
7056.2.a.by \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(+\) \(+\) \(q+3q^{5}+3q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots\)
7056.2.a.bz \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{5}+3q^{11}+4q^{13}-4q^{19}+4q^{25}+\cdots\)
7056.2.a.ca \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{5}-4q^{11}-4q^{13}+4q^{19}+11q^{25}+\cdots\)
7056.2.a.cb \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(4\) \(0\) \(+\) \(+\) \(+\) \(q+4q^{5}-3q^{13}-4q^{17}-7q^{19}-4q^{23}+\cdots\)
7056.2.a.cc \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(4\) \(0\) \(+\) \(+\) \(-\) \(q+4q^{5}+3q^{13}-4q^{17}+7q^{19}+4q^{23}+\cdots\)
7056.2.a.cd \(1\) \(56.342\) \(\Q\) None \(0\) \(0\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{5}+2q^{11}+6q^{13}-4q^{17}-4q^{19}+\cdots\)
7056.2.a.ce \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(q+(-2+\beta )q^{5}+(-2-2\beta )q^{11}+3\beta q^{13}+\cdots\)
7056.2.a.cf \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) \(-\) \(-\) \(+\) \(q+(-2+\beta )q^{5}-2q^{11}+(4+\beta )q^{13}+\cdots\)
7056.2.a.cg \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(q+(-2+\beta )q^{5}+(2-2\beta )q^{11}-\beta q^{13}+\cdots\)
7056.2.a.ch \(2\) \(56.342\) \(\Q(\sqrt{57}) \) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q-\beta q^{5}-\beta q^{11}+(-3+\beta )q^{13}-4q^{17}+\cdots\)
7056.2.a.ci \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+\beta q^{5}-4q^{11}+3\beta q^{13}-5\beta q^{17}+\cdots\)
7056.2.a.cj \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+\beta q^{5}-4q^{11}+\beta q^{13}-2\beta q^{17}+\cdots\)
7056.2.a.ck \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q+\beta q^{5}-2q^{11}+2\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cl \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+2\beta q^{5}-2q^{11}-\beta q^{17}-5\beta q^{19}+\cdots\)
7056.2.a.cm \(2\) \(56.342\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+\beta q^{5}-\beta q^{11}-2q^{13}-\beta q^{17}-4q^{19}+\cdots\)
7056.2.a.cn \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+\beta q^{5}+\beta q^{13}-\beta q^{17}-4q^{23}-3q^{25}+\cdots\)
7056.2.a.co \(2\) \(56.342\) \(\Q(\sqrt{7}) \) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+\beta q^{11}-\beta q^{23}-5q^{25}-2\beta q^{29}+\cdots\)
7056.2.a.cp \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+\beta q^{5}-\beta q^{13}-\beta q^{17}+4q^{23}-3q^{25}+\cdots\)
7056.2.a.cq \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q+\beta q^{5}+2q^{11}-2\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cr \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+\beta q^{5}+4q^{11}-3\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cs \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+\beta q^{5}+4q^{11}-3\beta q^{13}-5\beta q^{17}+\cdots\)
7056.2.a.ct \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+2\beta q^{5}+6q^{11}+4\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cu \(2\) \(56.342\) \(\Q(\sqrt{57}) \) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q+\beta q^{5}-\beta q^{11}+(3-\beta )q^{13}+4q^{17}+\cdots\)
7056.2.a.cv \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) \(-\) \(-\) \(+\) \(q+(2+\beta )q^{5}-2q^{11}+(-4+\beta )q^{13}+\cdots\)
7056.2.a.cw \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q+(2+\beta )q^{5}+(-2+2\beta )q^{11}+3\beta q^{13}+\cdots\)
7056.2.a.cx \(2\) \(56.342\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q+(2+\beta )q^{5}+(2+2\beta )q^{11}-\beta q^{13}+\cdots\)
7056.2.a.cy \(4\) \(56.342\) \(\Q(\sqrt{2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{5}+\beta _{3}q^{11}-3\beta _{1}q^{13}+\beta _{2}q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7056))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7056)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1764))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3528))\)\(^{\oplus 2}\)