Properties

Label 7440.2.a
Level $7440$
Weight $2$
Character orbit 7440.a
Rep. character $\chi_{7440}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $58$
Sturm bound $3072$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7440.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 58 \)
Sturm bound: \(3072\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7440))\).

Total New Old
Modular forms 1560 120 1440
Cusp forms 1513 120 1393
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.

\(2\)\(3\)\(5\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(8\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(52\)
Minus space\(-\)\(68\)

Trace form

\( 120q - 8q^{7} + 120q^{9} + O(q^{10}) \) \( 120q - 8q^{7} + 120q^{9} - 16q^{11} - 16q^{23} + 120q^{25} + 32q^{29} + 32q^{37} - 16q^{41} - 16q^{43} + 104q^{49} + 32q^{53} - 8q^{63} - 16q^{65} + 8q^{67} + 32q^{71} + 32q^{77} - 16q^{79} + 120q^{81} + 48q^{83} - 24q^{87} - 16q^{89} - 48q^{91} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7440))\) 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 31
7440.2.a.a \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
7440.2.a.b \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-2q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
7440.2.a.c \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots\)
7440.2.a.d \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{9}-2q^{13}+q^{15}-2q^{17}+\cdots\)
7440.2.a.e \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+2q^{7}+q^{9}+q^{15}+2q^{17}+\cdots\)
7440.2.a.f \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-4q^{7}+q^{9}-6q^{11}-6q^{13}+\cdots\)
7440.2.a.g \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-4q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
7440.2.a.h \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
7440.2.a.i \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}+6q^{17}+\cdots\)
7440.2.a.j \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
7440.2.a.k \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
7440.2.a.l \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
7440.2.a.m \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
7440.2.a.n \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
7440.2.a.o \(1\) \(59.409\) \(\Q\) None \(0\) \(-1\) \(1\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
7440.2.a.p \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(-3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-3q^{7}+q^{9}-5q^{11}-6q^{13}+\cdots\)
7440.2.a.q \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
7440.2.a.r \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+q^{9}+6q^{11}-2q^{13}+\cdots\)
7440.2.a.s \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-6q^{13}+\cdots\)
7440.2.a.t \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+2q^{7}+q^{9}+4q^{13}-q^{15}+\cdots\)
7440.2.a.u \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+2q^{7}+q^{9}+4q^{13}-q^{15}+\cdots\)
7440.2.a.v \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(-1\) \(3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+3q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
7440.2.a.w \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
7440.2.a.x \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-3q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
7440.2.a.y \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
7440.2.a.z \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}-4q^{17}+\cdots\)
7440.2.a.ba \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}+q^{15}+\cdots\)
7440.2.a.bb \(1\) \(59.409\) \(\Q\) None \(0\) \(1\) \(1\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+4q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
7440.2.a.bc \(2\) \(59.409\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(-1+\beta )q^{7}+q^{9}+4q^{11}+\cdots\)
7440.2.a.bd \(2\) \(59.409\) \(\Q(\sqrt{65}) \) None \(0\) \(-2\) \(-2\) \(1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
7440.2.a.be \(2\) \(59.409\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(4\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}-2\beta q^{11}+\cdots\)
7440.2.a.bf \(2\) \(59.409\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(-6\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+(-3+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7440.2.a.bg \(2\) \(59.409\) \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(2\) \(-1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
7440.2.a.bh \(2\) \(59.409\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(4\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+(2+\beta )q^{7}+q^{9}-2\beta q^{11}+\cdots\)
7440.2.a.bi \(2\) \(59.409\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(-1+\cdots)q^{13}+\cdots\)
7440.2.a.bj \(2\) \(59.409\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{13}+\cdots\)
7440.2.a.bk \(2\) \(59.409\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(6\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(3+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7440.2.a.bl \(2\) \(59.409\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(2\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-\beta q^{7}+q^{9}-\beta q^{11}+2q^{13}+\cdots\)
7440.2.a.bm \(3\) \(59.409\) 3.3.148.1 None \(0\) \(-3\) \(-3\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
7440.2.a.bn \(3\) \(59.409\) 3.3.404.1 None \(0\) \(-3\) \(-3\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+(1-\beta _{2})q^{7}+q^{9}-2\beta _{2}q^{11}+\cdots\)
7440.2.a.bo \(3\) \(59.409\) 3.3.148.1 None \(0\) \(-3\) \(-3\) \(2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(1-\beta _{1})q^{7}+q^{9}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.bp \(3\) \(59.409\) 3.3.148.1 None \(0\) \(-3\) \(3\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(-1+\beta _{1})q^{7}+q^{9}-2q^{11}+\cdots\)
7440.2.a.bq \(3\) \(59.409\) 3.3.7636.1 None \(0\) \(-3\) \(3\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}-2q^{11}+\cdots\)
7440.2.a.br \(3\) \(59.409\) 3.3.148.1 None \(0\) \(-3\) \(3\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(2\beta _{1}+\beta _{2})q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
7440.2.a.bs \(3\) \(59.409\) 3.3.564.1 None \(0\) \(3\) \(-3\) \(-8\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+(-3+\beta _{1})q^{7}+q^{9}-2\beta _{1}q^{11}+\cdots\)
7440.2.a.bt \(3\) \(59.409\) 3.3.564.1 None \(0\) \(3\) \(-3\) \(-4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
7440.2.a.bu \(3\) \(59.409\) 3.3.404.1 None \(0\) \(3\) \(-3\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(1+\beta _{1})q^{7}+q^{9}-4q^{11}+\cdots\)
7440.2.a.bv \(3\) \(59.409\) 3.3.316.1 None \(0\) \(3\) \(3\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+(-1-\beta _{2})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.bw \(3\) \(59.409\) 3.3.568.1 None \(0\) \(3\) \(3\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
7440.2.a.bx \(4\) \(59.409\) 4.4.78292.1 None \(0\) \(4\) \(-4\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-\beta _{1}q^{7}+q^{9}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
7440.2.a.by \(4\) \(59.409\) 4.4.70164.1 None \(0\) \(4\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+\beta _{3}q^{7}+q^{9}+2q^{11}+\cdots\)
7440.2.a.bz \(4\) \(59.409\) 4.4.8468.1 None \(0\) \(4\) \(4\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+(-1+\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots\)
7440.2.a.ca \(4\) \(59.409\) 4.4.92692.1 None \(0\) \(4\) \(4\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+\beta _{2}q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.cb \(4\) \(59.409\) 4.4.224148.1 None \(0\) \(4\) \(4\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+(1-\beta _{1})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.cc \(4\) \(59.409\) 4.4.17428.1 None \(0\) \(4\) \(4\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+(1-\beta _{3})q^{7}+q^{9}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
7440.2.a.cd \(5\) \(59.409\) 5.5.2294036.1 None \(0\) \(-5\) \(-5\) \(-3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7440.2.a.ce \(5\) \(59.409\) 5.5.5547956.1 None \(0\) \(-5\) \(-5\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(\beta _{1}+\beta _{3})q^{7}+q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots\)
7440.2.a.cf \(5\) \(59.409\) 5.5.24504404.1 None \(0\) \(-5\) \(5\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+\beta _{4}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7440))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7440)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(124))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(248))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(372))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(496))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(620))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(744))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(930))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1488))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1860))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3720))\)\(^{\oplus 2}\)