Properties

Label 7280.2.a
Level $7280$
Weight $2$
Character orbit 7280.a
Rep. character $\chi_{7280}(1,\cdot)$
Character field $\Q$
Dimension $144$
Newform subspaces $59$
Sturm bound $2688$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 7280 = 2^{4} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7280.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 59 \)
Sturm bound: \(2688\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(3\), \(11\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7280))\).

Total New Old
Modular forms 1368 144 1224
Cusp forms 1321 144 1177
Eisenstein series 47 0 47

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

\(2\)\(5\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(10\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(10\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(10\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(12\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(11\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(62\)
Minus space\(-\)\(82\)

Trace form

\( 144 q - 4 q^{7} + 128 q^{9} + O(q^{10}) \) \( 144 q - 4 q^{7} + 128 q^{9} - 8 q^{11} - 8 q^{15} - 16 q^{17} - 16 q^{19} - 8 q^{23} + 144 q^{25} + 16 q^{29} - 16 q^{31} + 16 q^{37} + 16 q^{41} - 8 q^{43} + 144 q^{49} - 16 q^{51} + 16 q^{53} + 32 q^{61} - 20 q^{63} - 16 q^{67} + 32 q^{69} + 40 q^{71} - 48 q^{73} + 16 q^{77} - 56 q^{79} + 112 q^{81} + 48 q^{83} + 32 q^{85} - 16 q^{89} - 48 q^{97} - 40 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7280))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 7 13
7280.2.a.a $1$ $58.131$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ \(q-2q^{3}-q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots\)
7280.2.a.b $1$ $58.131$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ \(q-2q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
7280.2.a.c $1$ $58.131$ \(\Q\) None \(0\) \(-2\) \(-1\) \(1\) $+$ $+$ $-$ $+$ \(q-2q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
7280.2.a.d $1$ $58.131$ \(\Q\) None \(0\) \(-2\) \(1\) \(1\) $+$ $-$ $-$ $+$ \(q-2q^{3}+q^{5}+q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
7280.2.a.e $1$ $58.131$ \(\Q\) None \(0\) \(-2\) \(1\) \(1\) $+$ $-$ $-$ $+$ \(q-2q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
7280.2.a.f $1$ $58.131$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ \(q-q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
7280.2.a.g $1$ $58.131$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $-$ $-$ $+$ $-$ \(q-q^{3}+q^{5}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
7280.2.a.h $1$ $58.131$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ \(q-q^{5}-q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots\)
7280.2.a.i $1$ $58.131$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ \(q-q^{5}-q^{7}-3q^{9}-q^{13}+6q^{17}+\cdots\)
7280.2.a.j $1$ $58.131$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $-$ $-$ \(q-q^{5}+q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots\)
7280.2.a.k $1$ $58.131$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $-$ $+$ \(q-q^{5}+q^{7}-3q^{9}-q^{13}-2q^{17}+\cdots\)
7280.2.a.l $1$ $58.131$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $-$ $-$ \(q-q^{5}+q^{7}-3q^{9}+6q^{11}+q^{13}+\cdots\)
7280.2.a.m $1$ $58.131$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $+$ $+$ \(q+q^{5}-q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots\)
7280.2.a.n $1$ $58.131$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $+$ $+$ \(q+q^{5}-q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots\)
7280.2.a.o $1$ $58.131$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ \(q+q^{5}+q^{7}-3q^{9}+q^{13}-6q^{17}+\cdots\)
7280.2.a.p $1$ $58.131$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ \(q+q^{3}-q^{5}-q^{7}-2q^{9}+5q^{11}-q^{13}+\cdots\)
7280.2.a.q $1$ $58.131$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $+$ $+$ $-$ $+$ \(q+q^{3}-q^{5}+q^{7}-2q^{9}-5q^{11}-q^{13}+\cdots\)
7280.2.a.r $1$ $58.131$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $+$ \(q+q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots\)
7280.2.a.s $1$ $58.131$ \(\Q\) None \(0\) \(2\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ \(q+2q^{3}-q^{5}-q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
7280.2.a.t $1$ $58.131$ \(\Q\) None \(0\) \(2\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ \(q+2q^{3}-q^{5}-q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
7280.2.a.u $1$ $58.131$ \(\Q\) None \(0\) \(2\) \(1\) \(-1\) $+$ $-$ $+$ $-$ \(q+2q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
7280.2.a.v $1$ $58.131$ \(\Q\) None \(0\) \(2\) \(1\) \(1\) $-$ $-$ $-$ $+$ \(q+2q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
7280.2.a.w $1$ $58.131$ \(\Q\) None \(0\) \(3\) \(-1\) \(1\) $-$ $+$ $-$ $-$ \(q+3q^{3}-q^{5}+q^{7}+6q^{9}-3q^{11}+\cdots\)
7280.2.a.x $2$ $58.131$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-2\) $-$ $+$ $+$ $-$ \(q+(-1+\beta )q^{3}-q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
7280.2.a.y $2$ $58.131$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(2\) $-$ $+$ $-$ $-$ \(q+(-1-\beta )q^{3}-q^{5}+q^{7}+(3+2\beta )q^{9}+\cdots\)
7280.2.a.z $2$ $58.131$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(2\) \(-2\) $+$ $-$ $+$ $-$ \(q-\beta q^{3}+q^{5}-q^{7}+(-2+\beta )q^{9}+4\beta q^{11}+\cdots\)
7280.2.a.ba $2$ $58.131$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(2\) \(2\) $-$ $-$ $-$ $-$ \(q-\beta q^{3}+q^{5}+q^{7}+(-2+\beta )q^{9}-2\beta q^{11}+\cdots\)
7280.2.a.bb $2$ $58.131$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(2\) $-$ $-$ $-$ $-$ \(q-\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots\)
7280.2.a.bc $2$ $58.131$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $+$ $-$ \(q+\beta q^{3}+q^{5}-q^{7}+5q^{9}-4q^{11}+\cdots\)
7280.2.a.bd $2$ $58.131$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $-$ \(q+q^{5}+q^{7}-3q^{9}+\beta q^{11}+q^{13}+\cdots\)
7280.2.a.be $2$ $58.131$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(-2\) \(-2\) $-$ $+$ $+$ $+$ \(q+\beta q^{3}-q^{5}-q^{7}+\beta q^{9}+2q^{11}+\cdots\)
7280.2.a.bf $2$ $58.131$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(2\) $-$ $+$ $-$ $+$ \(q+\beta q^{3}-q^{5}+q^{7}+(-2+\beta )q^{9}+2\beta q^{11}+\cdots\)
7280.2.a.bg $2$ $58.131$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-2\) \(2\) $-$ $+$ $-$ $+$ \(q+\beta q^{3}-q^{5}+q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
7280.2.a.bh $2$ $58.131$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(2\) \(-2\) $+$ $-$ $+$ $+$ \(q+\beta q^{3}+q^{5}-q^{7}+\beta q^{9}+(2-2\beta )q^{11}+\cdots\)
7280.2.a.bi $2$ $58.131$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(2\) \(2\) $+$ $-$ $-$ $+$ \(q+\beta q^{3}+q^{5}+q^{7}+(-2+\beta )q^{9}-q^{13}+\cdots\)
7280.2.a.bj $2$ $58.131$ \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(-2\) \(-2\) $-$ $+$ $+$ $-$ \(q+(1+\beta )q^{3}-q^{5}-q^{7}+(1+3\beta )q^{9}+\cdots\)
7280.2.a.bk $2$ $58.131$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(2\) \(-2\) $-$ $-$ $+$ $-$ \(q+(1+\beta )q^{3}+q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots\)
7280.2.a.bl $3$ $58.131$ 3.3.229.1 None \(0\) \(-1\) \(3\) \(-3\) $-$ $-$ $+$ $+$ \(q+\beta _{2}q^{3}+q^{5}-q^{7}+(1-\beta _{1})q^{9}+(-2+\cdots)q^{11}+\cdots\)
7280.2.a.bm $3$ $58.131$ 3.3.1573.1 None \(0\) \(-1\) \(3\) \(3\) $+$ $-$ $-$ $+$ \(q-\beta _{1}q^{3}+q^{5}+q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.bn $3$ $58.131$ 3.3.1101.1 None \(0\) \(1\) \(-3\) \(-3\) $+$ $+$ $+$ $+$ \(q+\beta _{1}q^{3}-q^{5}-q^{7}+(4-\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.bo $3$ $58.131$ 3.3.568.1 None \(0\) \(1\) \(3\) \(3\) $-$ $-$ $-$ $+$ \(q-\beta _{2}q^{3}+q^{5}+q^{7}+(3-\beta _{1})q^{9}+(-2+\cdots)q^{11}+\cdots\)
7280.2.a.bp $3$ $58.131$ 3.3.229.1 None \(0\) \(2\) \(-3\) \(3\) $+$ $+$ $-$ $-$ \(q+(1+\beta _{2})q^{3}-q^{5}+q^{7}+(1+\beta _{1})q^{9}+\cdots\)
7280.2.a.bq $4$ $58.131$ 4.4.1957.1 None \(0\) \(-4\) \(4\) \(4\) $-$ $-$ $-$ $+$ \(q+(-1+\beta _{2})q^{3}+q^{5}+q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
7280.2.a.br $4$ $58.131$ 4.4.4913.1 None \(0\) \(-3\) \(-4\) \(4\) $+$ $+$ $-$ $-$ \(q+(-1+\beta _{1})q^{3}-q^{5}+q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
7280.2.a.bs $4$ $58.131$ 4.4.23724.1 None \(0\) \(-1\) \(-4\) \(-4\) $+$ $+$ $+$ $-$ \(q+\beta _{1}q^{3}-q^{5}-q^{7}+(1+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
7280.2.a.bt $4$ $58.131$ 4.4.2225.1 None \(0\) \(-1\) \(-4\) \(4\) $+$ $+$ $-$ $+$ \(q-\beta _{1}q^{3}-q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.bu $4$ $58.131$ 4.4.50908.1 None \(0\) \(-1\) \(4\) \(-4\) $-$ $-$ $+$ $+$ \(q-\beta _{3}q^{3}+q^{5}-q^{7}+(2-\beta _{1}+\beta _{3})q^{9}+\cdots\)
7280.2.a.bv $4$ $58.131$ 4.4.24197.1 None \(0\) \(0\) \(-4\) \(-4\) $+$ $+$ $+$ $-$ \(q-\beta _{1}q^{3}-q^{5}-q^{7}+\beta _{2}q^{9}+(\beta _{2}-\beta _{3})q^{11}+\cdots\)
7280.2.a.bw $4$ $58.131$ 4.4.12197.1 None \(0\) \(0\) \(-4\) \(4\) $-$ $+$ $-$ $-$ \(q+\beta _{1}q^{3}-q^{5}+q^{7}+(2-\beta _{3})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
7280.2.a.bx $4$ $58.131$ 4.4.24197.1 None \(0\) \(0\) \(4\) \(4\) $+$ $-$ $-$ $-$ \(q-\beta _{2}q^{3}+q^{5}+q^{7}+(4+\beta _{1})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
7280.2.a.by $4$ $58.131$ 4.4.30972.1 None \(0\) \(1\) \(-4\) \(4\) $-$ $+$ $-$ $-$ \(q+\beta _{1}q^{3}-q^{5}+q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7280.2.a.bz $4$ $58.131$ 4.4.13676.1 None \(0\) \(1\) \(-4\) \(4\) $+$ $+$ $-$ $+$ \(q+\beta _{1}q^{3}-q^{5}+q^{7}+(3+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
7280.2.a.ca $4$ $58.131$ 4.4.2225.1 None \(0\) \(1\) \(4\) \(4\) $+$ $-$ $-$ $-$ \(q+\beta _{1}q^{3}+q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.cb $4$ $58.131$ 4.4.27004.1 None \(0\) \(3\) \(4\) \(4\) $-$ $-$ $-$ $+$ \(q+(1-\beta _{1})q^{3}+q^{5}+q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7280.2.a.cc $5$ $58.131$ 5.5.1194649.1 None \(0\) \(0\) \(-5\) \(-5\) $+$ $+$ $+$ $+$ \(q+\beta _{1}q^{3}-q^{5}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7280.2.a.cd $5$ $58.131$ 5.5.2112217.1 None \(0\) \(0\) \(5\) \(-5\) $+$ $-$ $+$ $+$ \(q+\beta _{1}q^{3}+q^{5}-q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
7280.2.a.ce $6$ $58.131$ 6.6.45853772.1 None \(0\) \(0\) \(6\) \(-6\) $-$ $-$ $+$ $-$ \(q-\beta _{5}q^{3}+q^{5}-q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7280.2.a.cf $7$ $58.131$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-4\) \(7\) \(-7\) $+$ $-$ $+$ $-$ \(q+(-1+\beta _{1})q^{3}+q^{5}-q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
7280.2.a.cg $7$ $58.131$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(-7\) \(-7\) $-$ $+$ $+$ $+$ \(q-\beta _{5}q^{3}-q^{5}-q^{7}+(3-\beta _{4})q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(910))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1040))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1820))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3640))\)\(^{\oplus 2}\)