Properties

Label 2352.4.a
Level $2352$
Weight $4$
Character orbit 2352.a
Rep. character $\chi_{2352}(1,\cdot)$
Character field $\Q$
Dimension $123$
Newform subspaces $70$
Sturm bound $1792$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 70 \)
Sturm bound: \(1792\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2352))\).

Total New Old
Modular forms 1392 123 1269
Cusp forms 1296 123 1173
Eisenstein series 96 0 96

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.
\(+\)\(+\)\(+\)\(+\)\(15\)
\(+\)\(+\)\(-\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(13\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(16\)
\(-\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(+\)\(16\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(64\)
Minus space\(-\)\(59\)

Trace form

\( 123q + 3q^{3} + 2q^{5} + 1107q^{9} + O(q^{10}) \) \( 123q + 3q^{3} + 2q^{5} + 1107q^{9} + 20q^{11} - 46q^{13} + 30q^{15} - 26q^{17} + 36q^{19} + 248q^{23} + 3013q^{25} + 27q^{27} + 58q^{29} - 288q^{31} + 12q^{33} + 74q^{37} - 54q^{39} - 178q^{41} + 320q^{43} + 18q^{45} - 168q^{47} - 678q^{51} - 1054q^{53} - 2048q^{55} + 84q^{57} - 628q^{59} - 734q^{61} - 68q^{65} - 96q^{67} - 264q^{69} - 32q^{71} + 14q^{73} - 27q^{75} + 1684q^{79} + 9963q^{81} - 964q^{83} - 1228q^{85} + 162q^{87} + 1646q^{89} - 456q^{93} + 4448q^{95} + 918q^{97} + 180q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2352))\) 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
2352.4.a.a \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(-18\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}-18q^{5}+9q^{9}+72q^{11}+34q^{13}+\cdots\)
2352.4.a.b \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(-12\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}-12q^{5}+9q^{9}-20q^{11}+84q^{13}+\cdots\)
2352.4.a.c \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(-7\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{3}-7q^{5}+9q^{9}-7q^{11}+52q^{13}+\cdots\)
2352.4.a.d \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(-6\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}-6q^{5}+9q^{9}-6^{2}q^{11}-62q^{13}+\cdots\)
2352.4.a.e \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(-6\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}-6q^{5}+9q^{9}-12q^{11}-38q^{13}+\cdots\)
2352.4.a.f \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(-6\) \(0\) \(-\) \(+\) \(+\) \(q-3q^{3}-6q^{5}+9q^{9}+30q^{11}+53q^{13}+\cdots\)
2352.4.a.g \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}-4q^{5}+9q^{9}+20q^{11}+4q^{13}+\cdots\)
2352.4.a.h \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(-4\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{3}-4q^{5}+9q^{9}+26q^{11}-2q^{13}+\cdots\)
2352.4.a.i \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(q-3q^{3}-3q^{5}+9q^{9}+15q^{11}-2^{6}q^{13}+\cdots\)
2352.4.a.j \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{3}-2q^{5}+9q^{9}+18q^{11}-33q^{13}+\cdots\)
2352.4.a.k \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{3}+2q^{5}+9q^{9}-12q^{11}+66q^{13}+\cdots\)
2352.4.a.l \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(4\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}+4q^{5}+9q^{9}-62q^{11}+62q^{13}+\cdots\)
2352.4.a.m \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(8\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}+8q^{5}+9q^{9}-40q^{11}+4q^{13}+\cdots\)
2352.4.a.n \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(10\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{3}+10q^{5}+9q^{9}+12q^{11}-30q^{13}+\cdots\)
2352.4.a.o \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(11\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{3}+11q^{5}+9q^{9}-39q^{11}+2^{5}q^{13}+\cdots\)
2352.4.a.p \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(12\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{3}+12q^{5}+9q^{9}+60q^{11}+44q^{13}+\cdots\)
2352.4.a.q \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(15\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}+15q^{5}+9q^{9}+9q^{11}+88q^{13}+\cdots\)
2352.4.a.r \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(18\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}+18q^{5}+9q^{9}+6^{2}q^{11}+34q^{13}+\cdots\)
2352.4.a.s \(1\) \(138.772\) \(\Q\) None \(0\) \(-3\) \(18\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}+18q^{5}+9q^{9}+50q^{11}-6^{2}q^{13}+\cdots\)
2352.4.a.t \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(-18\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}-18q^{5}+9q^{9}+50q^{11}+6^{2}q^{13}+\cdots\)
2352.4.a.u \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(-15\) \(0\) \(-\) \(-\) \(+\) \(q+3q^{3}-15q^{5}+9q^{9}+9q^{11}-88q^{13}+\cdots\)
2352.4.a.v \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(-14\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}-14q^{5}+9q^{9}-4q^{11}-54q^{13}+\cdots\)
2352.4.a.w \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(-14\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{3}-14q^{5}+9q^{9}+28q^{11}+74q^{13}+\cdots\)
2352.4.a.x \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(-12\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{3}-12q^{5}+9q^{9}+60q^{11}-44q^{13}+\cdots\)
2352.4.a.y \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(-11\) \(0\) \(+\) \(-\) \(+\) \(q+3q^{3}-11q^{5}+9q^{9}-39q^{11}-2^{5}q^{13}+\cdots\)
2352.4.a.z \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(-8\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}-8q^{5}+9q^{9}-40q^{11}-4q^{13}+\cdots\)
2352.4.a.ba \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}-2q^{5}+9q^{9}+8q^{11}+42q^{13}+\cdots\)
2352.4.a.bb \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(2\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{3}+2q^{5}+9q^{9}-52q^{11}-86q^{13}+\cdots\)
2352.4.a.bc \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+3q^{3}+2q^{5}+9q^{9}+18q^{11}+33q^{13}+\cdots\)
2352.4.a.bd \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}+3q^{5}+9q^{9}+15q^{11}+2^{6}q^{13}+\cdots\)
2352.4.a.be \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}+4q^{5}+9q^{9}+20q^{11}-4q^{13}+\cdots\)
2352.4.a.bf \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(6\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}+6q^{5}+9q^{9}+30q^{11}-53q^{13}+\cdots\)
2352.4.a.bg \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(7\) \(0\) \(+\) \(-\) \(+\) \(q+3q^{3}+7q^{5}+9q^{9}-7q^{11}-52q^{13}+\cdots\)
2352.4.a.bh \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(10\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{3}+10q^{5}+9q^{9}+52q^{11}+10q^{13}+\cdots\)
2352.4.a.bi \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(12\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}+12q^{5}+9q^{9}-20q^{11}-84q^{13}+\cdots\)
2352.4.a.bj \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(16\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{3}+2^{4}q^{5}+9q^{9}+18q^{11}+54q^{13}+\cdots\)
2352.4.a.bk \(1\) \(138.772\) \(\Q\) None \(0\) \(3\) \(18\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}+18q^{5}+9q^{9}-6^{2}q^{11}+10q^{13}+\cdots\)
2352.4.a.bl \(2\) \(138.772\) \(\Q(\sqrt{2}) \) None \(0\) \(-6\) \(-20\) \(0\) \(-\) \(+\) \(+\) \(q-3q^{3}+(-10+7\beta )q^{5}+9q^{9}+(10+\cdots)q^{11}+\cdots\)
2352.4.a.bm \(2\) \(138.772\) \(\Q(\sqrt{137}) \) None \(0\) \(-6\) \(-18\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{3}+(-9-\beta )q^{5}+9q^{9}+(-29+\cdots)q^{11}+\cdots\)
2352.4.a.bn \(2\) \(138.772\) \(\Q(\sqrt{2}) \) None \(0\) \(-6\) \(-12\) \(0\) \(-\) \(+\) \(+\) \(q-3q^{3}+(-6+\beta )q^{5}+9q^{9}+(2+6\beta )q^{11}+\cdots\)
2352.4.a.bo \(2\) \(138.772\) \(\Q(\sqrt{505}) \) None \(0\) \(-6\) \(-9\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{3}+(-4-\beta )q^{5}+9q^{9}-5\beta q^{11}+\cdots\)
2352.4.a.bp \(2\) \(138.772\) \(\Q(\sqrt{57}) \) None \(0\) \(-6\) \(3\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}+(2+\beta )q^{5}+9q^{9}+(26+\beta )q^{11}+\cdots\)
2352.4.a.bq \(2\) \(138.772\) \(\Q(\sqrt{1345}) \) None \(0\) \(-6\) \(5\) \(0\) \(-\) \(+\) \(+\) \(q-3q^{3}+(3-\beta )q^{5}+9q^{9}+(-33-\beta )q^{11}+\cdots\)
2352.4.a.br \(2\) \(138.772\) \(\Q(\sqrt{337}) \) None \(0\) \(-6\) \(6\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{3}+(3+\beta )q^{5}+9q^{9}+(-13-\beta )q^{11}+\cdots\)
2352.4.a.bs \(2\) \(138.772\) \(\Q(\sqrt{113}) \) None \(0\) \(-6\) \(6\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{3}+(3+\beta )q^{5}+9q^{9}+(-1-3\beta )q^{11}+\cdots\)
2352.4.a.bt \(2\) \(138.772\) \(\Q(\sqrt{193}) \) None \(0\) \(-6\) \(11\) \(0\) \(-\) \(+\) \(+\) \(q-3q^{3}+(6-\beta )q^{5}+9q^{9}+(6-7\beta )q^{11}+\cdots\)
2352.4.a.bu \(2\) \(138.772\) \(\Q(\sqrt{2}) \) None \(0\) \(-6\) \(12\) \(0\) \(-\) \(+\) \(+\) \(q-3q^{3}+(6+\beta )q^{5}+9q^{9}+(-2-6\beta )q^{11}+\cdots\)
2352.4.a.bv \(2\) \(138.772\) \(\Q(\sqrt{177}) \) None \(0\) \(6\) \(-14\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{3}+(-7-\beta )q^{5}+9q^{9}+(-9+\cdots)q^{11}+\cdots\)
2352.4.a.bw \(2\) \(138.772\) \(\Q(\sqrt{2}) \) None \(0\) \(6\) \(-12\) \(0\) \(-\) \(-\) \(+\) \(q+3q^{3}+(-6+\beta )q^{5}+9q^{9}+(-2+\cdots)q^{11}+\cdots\)
2352.4.a.bx \(2\) \(138.772\) \(\Q(\sqrt{193}) \) None \(0\) \(6\) \(-11\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}+(-5-\beta )q^{5}+9q^{9}+(-1+\cdots)q^{11}+\cdots\)
2352.4.a.by \(2\) \(138.772\) \(\Q(\sqrt{113}) \) None \(0\) \(6\) \(-6\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{3}+(-3-\beta )q^{5}+9q^{9}+(-1+\cdots)q^{11}+\cdots\)
2352.4.a.bz \(2\) \(138.772\) \(\Q(\sqrt{57}) \) None \(0\) \(6\) \(-6\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}+(-3-\beta )q^{5}+9q^{9}+(3-5\beta )q^{11}+\cdots\)
2352.4.a.ca \(2\) \(138.772\) \(\Q(\sqrt{1345}) \) None \(0\) \(6\) \(-5\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}+(-2-\beta )q^{5}+9q^{9}+(-34+\cdots)q^{11}+\cdots\)
2352.4.a.cb \(2\) \(138.772\) \(\Q(\sqrt{57}) \) None \(0\) \(6\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q+3q^{3}+(-2-\beta )q^{5}+9q^{9}+(26+\beta )q^{11}+\cdots\)
2352.4.a.cc \(2\) \(138.772\) \(\Q(\sqrt{505}) \) None \(0\) \(6\) \(9\) \(0\) \(+\) \(-\) \(+\) \(q+3q^{3}+(5-\beta )q^{5}+9q^{9}+(-5+5\beta )q^{11}+\cdots\)
2352.4.a.cd \(2\) \(138.772\) \(\Q(\sqrt{2}) \) None \(0\) \(6\) \(12\) \(0\) \(-\) \(-\) \(+\) \(q+3q^{3}+(6+\beta )q^{5}+9q^{9}+(2-6\beta )q^{11}+\cdots\)
2352.4.a.ce \(2\) \(138.772\) \(\Q(\sqrt{137}) \) None \(0\) \(6\) \(18\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{3}+(9-\beta )q^{5}+9q^{9}+(-29-3\beta )q^{11}+\cdots\)
2352.4.a.cf \(2\) \(138.772\) \(\Q(\sqrt{2}) \) None \(0\) \(6\) \(20\) \(0\) \(-\) \(-\) \(+\) \(q+3q^{3}+(10+7\beta )q^{5}+9q^{9}+(10-24\beta )q^{11}+\cdots\)
2352.4.a.cg \(3\) \(138.772\) 3.3.57516.1 None \(0\) \(-9\) \(-11\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}+(-4-\beta _{2})q^{5}+9q^{9}+(-11+\cdots)q^{11}+\cdots\)
2352.4.a.ch \(3\) \(138.772\) 3.3.58461.1 None \(0\) \(-9\) \(-11\) \(0\) \(+\) \(+\) \(+\) \(q-3q^{3}+(-4-\beta _{1})q^{5}+9q^{9}+(6-\beta _{1}+\cdots)q^{11}+\cdots\)
2352.4.a.ci \(3\) \(138.772\) 3.3.57516.1 None \(0\) \(9\) \(11\) \(0\) \(-\) \(-\) \(+\) \(q+3q^{3}+(4+\beta _{2})q^{5}+9q^{9}+(-11+\cdots)q^{11}+\cdots\)
2352.4.a.cj \(3\) \(138.772\) 3.3.58461.1 None \(0\) \(9\) \(11\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{3}+(4+\beta _{1})q^{5}+9q^{9}+(6-\beta _{1}+\cdots)q^{11}+\cdots\)
2352.4.a.ck \(4\) \(138.772\) 4.4.145408.2 None \(0\) \(-12\) \(-8\) \(0\) \(+\) \(+\) \(+\) \(q-3q^{3}+(-2+\beta _{2}-3\beta _{3})q^{5}+9q^{9}+\cdots\)
2352.4.a.cl \(4\) \(138.772\) 4.4.136768.1 None \(0\) \(-12\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-3q^{3}+\beta _{1}q^{5}+9q^{9}+(-3\beta _{1}+\beta _{3})q^{11}+\cdots\)
2352.4.a.cm \(4\) \(138.772\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-12\) \(4\) \(0\) \(+\) \(+\) \(+\) \(q-3q^{3}+(1+\beta _{1})q^{5}+9q^{9}+(-3-2\beta _{1}+\cdots)q^{11}+\cdots\)
2352.4.a.cn \(4\) \(138.772\) 4.4.391168.1 None \(0\) \(-12\) \(8\) \(0\) \(+\) \(+\) \(+\) \(q-3q^{3}+(2+\beta _{1})q^{5}+9q^{9}+(-10+\cdots)q^{11}+\cdots\)
2352.4.a.co \(4\) \(138.772\) 4.4.391168.1 None \(0\) \(12\) \(-8\) \(0\) \(+\) \(-\) \(+\) \(q+3q^{3}+(-2-\beta _{1})q^{5}+9q^{9}+(-10+\cdots)q^{11}+\cdots\)
2352.4.a.cp \(4\) \(138.772\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(12\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{3}+(-1-\beta _{1})q^{5}+9q^{9}+(-3+\cdots)q^{11}+\cdots\)
2352.4.a.cq \(4\) \(138.772\) 4.4.136768.1 None \(0\) \(12\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+3q^{3}-\beta _{1}q^{5}+9q^{9}+(-3\beta _{1}+\beta _{3})q^{11}+\cdots\)
2352.4.a.cr \(4\) \(138.772\) 4.4.145408.2 None \(0\) \(12\) \(8\) \(0\) \(+\) \(-\) \(+\) \(q+3q^{3}+(2+\beta _{2}+3\beta _{3})q^{5}+9q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2352))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2352)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 2}\)