Properties

Label 6384.2.a
Level $6384$
Weight $2$
Character orbit 6384.a
Rep. character $\chi_{6384}(1,\cdot)$
Character field $\Q$
Dimension $108$
Newform subspaces $58$
Sturm bound $2560$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 6384 = 2^{4} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6384.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 58 \)
Sturm bound: \(2560\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6384))\).

Total New Old
Modular forms 1304 108 1196
Cusp forms 1257 108 1149
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.

\(2\)\(3\)\(7\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(46\)
Minus space\(-\)\(62\)

Trace form

\( 108 q - 8 q^{5} - 4 q^{7} + 108 q^{9} + O(q^{10}) \) \( 108 q - 8 q^{5} - 4 q^{7} + 108 q^{9} - 8 q^{11} - 8 q^{13} + 8 q^{17} - 8 q^{23} + 116 q^{25} + 8 q^{29} + 8 q^{37} - 16 q^{39} + 8 q^{41} - 16 q^{43} - 8 q^{45} + 48 q^{47} + 108 q^{49} + 8 q^{53} - 32 q^{55} + 48 q^{59} - 8 q^{61} - 4 q^{63} + 48 q^{65} - 8 q^{67} - 8 q^{71} + 40 q^{73} - 32 q^{75} + 16 q^{77} + 40 q^{79} + 108 q^{81} - 16 q^{85} + 40 q^{89} + 8 q^{97} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6384))\) 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 19
6384.2.a.a \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(-4\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.b \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(-4\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}-4q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6384.2.a.c \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(-4\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}-4q^{5}+q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
6384.2.a.d \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{5}-q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
6384.2.a.e \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
6384.2.a.f \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.g \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6384.2.a.h \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6384.2.a.i \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
6384.2.a.j \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{7}+q^{9}-2q^{13}-8q^{17}+\cdots\)
6384.2.a.k \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
6384.2.a.l \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(2\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
6384.2.a.m \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(2\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
6384.2.a.n \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(2\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
6384.2.a.o \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(2\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+2q^{5}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
6384.2.a.p \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(4\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}+4q^{5}-q^{7}+q^{9}+2q^{11}-4q^{15}+\cdots\)
6384.2.a.q \(1\) \(50.976\) \(\Q\) None \(0\) \(-1\) \(4\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
6384.2.a.r \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(-4\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-4q^{5}+q^{7}+q^{9}-2q^{13}-4q^{15}+\cdots\)
6384.2.a.s \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
6384.2.a.t \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
6384.2.a.u \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
6384.2.a.v \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.w \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.x \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}+2q^{11}-4q^{17}+\cdots\)
6384.2.a.y \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6384.2.a.z \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6384.2.a.ba \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
6384.2.a.bb \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{7}+q^{9}-2q^{13}-q^{19}+q^{21}+\cdots\)
6384.2.a.bc \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6384.2.a.bd \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
6384.2.a.be \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(2\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
6384.2.a.bf \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(2\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6384.2.a.bg \(1\) \(50.976\) \(\Q\) None \(0\) \(1\) \(2\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
6384.2.a.bh \(2\) \(50.976\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-4\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+(-2+\beta )q^{5}+q^{7}+q^{9}-2\beta q^{11}+\cdots\)
6384.2.a.bi \(2\) \(50.976\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}+4q^{11}+\cdots\)
6384.2.a.bj \(2\) \(50.976\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
6384.2.a.bk \(2\) \(50.976\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+\beta q^{5}+q^{7}+q^{9}-2q^{13}-\beta q^{15}+\cdots\)
6384.2.a.bl \(2\) \(50.976\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
6384.2.a.bm \(2\) \(50.976\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
6384.2.a.bn \(2\) \(50.976\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
6384.2.a.bo \(2\) \(50.976\) \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(-2\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots\)
6384.2.a.bp \(2\) \(50.976\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}+2\beta q^{13}+\cdots\)
6384.2.a.bq \(2\) \(50.976\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}-\beta q^{13}+\cdots\)
6384.2.a.br \(2\) \(50.976\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
6384.2.a.bs \(2\) \(50.976\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{13}+\cdots\)
6384.2.a.bt \(3\) \(50.976\) 3.3.1016.1 None \(0\) \(-3\) \(0\) \(-3\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
6384.2.a.bu \(3\) \(50.976\) 3.3.404.1 None \(0\) \(-3\) \(0\) \(3\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.bv \(3\) \(50.976\) 3.3.316.1 None \(0\) \(-3\) \(0\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}+(1-\beta _{1})q^{11}+(-2+\cdots)q^{13}+\cdots\)
6384.2.a.bw \(3\) \(50.976\) 3.3.568.1 None \(0\) \(3\) \(0\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}-\beta _{1}q^{5}+q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.bx \(3\) \(50.976\) 3.3.148.1 None \(0\) \(3\) \(4\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.by \(4\) \(50.976\) 4.4.2225.1 None \(0\) \(-4\) \(4\) \(-4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+(1-\beta _{2})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
6384.2.a.bz \(4\) \(50.976\) 4.4.7232.1 None \(0\) \(-4\) \(4\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+\beta _{2}q^{11}+\cdots\)
6384.2.a.ca \(4\) \(50.976\) 4.4.13068.1 None \(0\) \(4\) \(-4\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}+(-1-\beta _{2})q^{5}-q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
6384.2.a.cb \(4\) \(50.976\) 4.4.9248.1 None \(0\) \(4\) \(0\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
6384.2.a.cc \(5\) \(50.976\) 5.5.1240016.1 None \(0\) \(-5\) \(-2\) \(-5\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
6384.2.a.cd \(5\) \(50.976\) 5.5.401584.1 None \(0\) \(-5\) \(2\) \(-5\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots\)
6384.2.a.ce \(5\) \(50.976\) 5.5.135076.1 None \(0\) \(5\) \(2\) \(-5\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+\beta _{4}q^{11}+\cdots\)
6384.2.a.cf \(5\) \(50.976\) 5.5.368464.1 None \(0\) \(5\) \(4\) \(-5\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+(1+\beta _{3})q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6384))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6384)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(798))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1596))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3192))\)\(^{\oplus 2}\)