Properties

Label 7600.2.a
Level $7600$
Weight $2$
Character orbit 7600.a
Rep. character $\chi_{7600}(1,\cdot)$
Character field $\Q$
Dimension $171$
Newform subspaces $66$
Sturm bound $2400$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 66 \)
Sturm bound: \(2400\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7600))\).

Total New Old
Modular forms 1236 171 1065
Cusp forms 1165 171 994
Eisenstein series 71 0 71

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

\(2\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(19\)
\(+\)\(+\)\(-\)\(-\)\(22\)
\(+\)\(-\)\(+\)\(-\)\(25\)
\(+\)\(-\)\(-\)\(+\)\(19\)
\(-\)\(+\)\(+\)\(-\)\(20\)
\(-\)\(+\)\(-\)\(+\)\(20\)
\(-\)\(-\)\(+\)\(+\)\(23\)
\(-\)\(-\)\(-\)\(-\)\(23\)
Plus space\(+\)\(81\)
Minus space\(-\)\(90\)

Trace form

\( 171q - 2q^{7} + 171q^{9} + O(q^{10}) \) \( 171q - 2q^{7} + 171q^{9} - 10q^{11} + 2q^{13} - 2q^{17} - 3q^{19} + 8q^{21} - 16q^{23} - 24q^{27} + 18q^{29} + 8q^{33} + 18q^{37} - 28q^{39} - 2q^{41} + 18q^{43} - 10q^{47} + 179q^{49} - 44q^{51} + 10q^{53} + 16q^{59} + 10q^{61} - 30q^{63} - 20q^{67} - 8q^{69} - 12q^{71} - 2q^{73} - 8q^{77} - 8q^{79} + 163q^{81} - 8q^{83} + 12q^{87} - 18q^{89} - 8q^{91} + 8q^{93} - 10q^{97} - 10q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7600))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 19
7600.2.a.a \(1\) \(60.686\) \(\Q\) None \(0\) \(-3\) \(0\) \(-5\) \(-\) \(+\) \(+\) \(q-3q^{3}-5q^{7}+6q^{9}+4q^{11}+q^{13}+\cdots\)
7600.2.a.b \(1\) \(60.686\) \(\Q\) None \(0\) \(-2\) \(0\) \(-3\) \(+\) \(+\) \(-\) \(q-2q^{3}-3q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots\)
7600.2.a.c \(1\) \(60.686\) \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-2q^{3}-q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
7600.2.a.d \(1\) \(60.686\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-2q^{3}+q^{9}+4q^{11}-4q^{13}+2q^{17}+\cdots\)
7600.2.a.e \(1\) \(60.686\) \(\Q\) None \(0\) \(-2\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q-2q^{3}+2q^{7}+q^{9}-4q^{11}-8q^{17}+\cdots\)
7600.2.a.f \(1\) \(60.686\) \(\Q\) None \(0\) \(-2\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q-2q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
7600.2.a.g \(1\) \(60.686\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{3}-q^{7}-2q^{9}+3q^{13}+7q^{17}+\cdots\)
7600.2.a.h \(1\) \(60.686\) \(\Q\) None \(0\) \(-1\) \(0\) \(3\) \(-\) \(+\) \(-\) \(q-q^{3}+3q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
7600.2.a.i \(1\) \(60.686\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q-2q^{7}-3q^{9}+4q^{11}-2q^{13}+4q^{17}+\cdots\)
7600.2.a.j \(1\) \(60.686\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-2q^{7}-3q^{9}+4q^{11}+4q^{13}-6q^{17}+\cdots\)
7600.2.a.k \(1\) \(60.686\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-3q^{9}+4q^{11}+6q^{13}+6q^{17}+q^{19}+\cdots\)
7600.2.a.l \(1\) \(60.686\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+2q^{7}-3q^{9}+4q^{11}+2q^{13}-4q^{17}+\cdots\)
7600.2.a.m \(1\) \(60.686\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}-2q^{9}+q^{13}+3q^{17}+\cdots\)
7600.2.a.n \(1\) \(60.686\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}-2q^{9}+6q^{11}-5q^{13}+\cdots\)
7600.2.a.o \(1\) \(60.686\) \(\Q\) None \(0\) \(1\) \(0\) \(3\) \(+\) \(+\) \(+\) \(q+q^{3}+3q^{7}-2q^{9}-2q^{11}-q^{13}+\cdots\)
7600.2.a.p \(1\) \(60.686\) \(\Q\) None \(0\) \(2\) \(0\) \(-3\) \(-\) \(+\) \(-\) \(q+2q^{3}-3q^{7}+q^{9}-5q^{11}+4q^{13}+\cdots\)
7600.2.a.q \(1\) \(60.686\) \(\Q\) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q+2q^{3}-2q^{7}+q^{9}-4q^{11}+8q^{17}+\cdots\)
7600.2.a.r \(1\) \(60.686\) \(\Q\) None \(0\) \(2\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q+2q^{3}+2q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
7600.2.a.s \(1\) \(60.686\) \(\Q\) None \(0\) \(2\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+2q^{3}+4q^{7}+q^{9}+4q^{11}-6q^{17}+\cdots\)
7600.2.a.t \(1\) \(60.686\) \(\Q\) None \(0\) \(3\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(q+3q^{3}-q^{7}+6q^{9}-4q^{11}-q^{13}+\cdots\)
7600.2.a.u \(2\) \(60.686\) \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q+(-2+\beta )q^{3}+(-2-2\beta )q^{7}+(3-4\beta )q^{9}+\cdots\)
7600.2.a.v \(2\) \(60.686\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(-6\) \(-\) \(-\) \(-\) \(q+(-1+\beta )q^{3}+(-3-\beta )q^{7}-2\beta q^{9}+\cdots\)
7600.2.a.w \(2\) \(60.686\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+(-1-\beta )q^{3}+2\beta q^{7}+(3+2\beta )q^{9}+\cdots\)
7600.2.a.x \(2\) \(60.686\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+(-1+\beta )q^{3}+(1-\beta )q^{7}-2\beta q^{9}+\cdots\)
7600.2.a.y \(2\) \(60.686\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q-\beta q^{3}-\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
7600.2.a.z \(2\) \(60.686\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q+\beta q^{3}+(-2+2\beta )q^{7}-q^{9}+(-2+\cdots)q^{11}+\cdots\)
7600.2.a.ba \(2\) \(60.686\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q+\beta q^{3}+2\beta q^{7}-q^{9}+(-2-2\beta )q^{11}+\cdots\)
7600.2.a.bb \(2\) \(60.686\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(-\) \(q+\beta q^{3}+(2+2\beta )q^{7}-q^{9}+(-2-2\beta )q^{11}+\cdots\)
7600.2.a.bc \(2\) \(60.686\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q+(1+\beta )q^{3}+(-1-\beta )q^{7}+2\beta q^{9}+\cdots\)
7600.2.a.bd \(2\) \(60.686\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+(1+\beta )q^{3}+(1+2\beta )q^{9}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
7600.2.a.be \(2\) \(60.686\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{3}-2\beta q^{7}+(3+2\beta )q^{9}+(1+\cdots)q^{13}+\cdots\)
7600.2.a.bf \(2\) \(60.686\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{3}+2q^{7}+(1+2\beta )q^{9}+2\beta q^{11}+\cdots\)
7600.2.a.bg \(2\) \(60.686\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(6\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{3}+(3-\beta )q^{7}+2\beta q^{9}-\beta q^{11}+\cdots\)
7600.2.a.bh \(3\) \(60.686\) 3.3.169.1 None \(0\) \(-2\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{1})q^{7}+(1+\cdots)q^{9}+\cdots\)
7600.2.a.bi \(3\) \(60.686\) 3.3.568.1 None \(0\) \(-2\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{1})q^{7}+(2+\cdots)q^{9}+\cdots\)
7600.2.a.bj \(3\) \(60.686\) 3.3.257.1 None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1})q^{7}+(1+\cdots)q^{9}+\cdots\)
7600.2.a.bk \(3\) \(60.686\) 3.3.993.1 None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
7600.2.a.bl \(3\) \(60.686\) 3.3.321.1 None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots\)
7600.2.a.bm \(3\) \(60.686\) 3.3.257.1 None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots\)
7600.2.a.bn \(3\) \(60.686\) \(\Q(\zeta_{14})^+\) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+(-1-\beta _{2})q^{3}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
7600.2.a.bo \(3\) \(60.686\) 3.3.568.1 None \(0\) \(-1\) \(0\) \(-5\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(-2-\beta _{2})q^{7}+(1+2\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.bp \(3\) \(60.686\) 3.3.316.1 None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}+(-1+2\beta _{1}-\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots\)
7600.2.a.bq \(3\) \(60.686\) 3.3.229.1 None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q+\beta _{2}q^{3}+\beta _{1}q^{7}+(1-\beta _{1})q^{9}+(-2+\cdots)q^{13}+\cdots\)
7600.2.a.br \(3\) \(60.686\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{3}+(-\beta _{1}+2\beta _{2})q^{7}+(-1+\beta _{2})q^{9}+\cdots\)
7600.2.a.bs \(3\) \(60.686\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(\beta _{1}-2\beta _{2})q^{7}+(-1+\beta _{2})q^{9}+\cdots\)
7600.2.a.bt \(3\) \(60.686\) 3.3.257.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-\beta _{2}q^{3}+\beta _{2}q^{7}+(\beta _{1}-\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
7600.2.a.bu \(3\) \(60.686\) 3.3.257.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{2}q^{3}-\beta _{2}q^{7}+(\beta _{1}-\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
7600.2.a.bv \(3\) \(60.686\) 3.3.961.1 None \(0\) \(1\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}+(2-\beta _{1}+\beta _{2})q^{7}+(5-\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.bw \(3\) \(60.686\) \(\Q(\zeta_{14})^+\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+(1-\beta _{1})q^{3}+(1-\beta _{1}+2\beta _{2})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.bx \(3\) \(60.686\) 3.3.148.1 None \(0\) \(2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+(1-\beta _{1})q^{3}+(\beta _{1}-\beta _{2})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.by \(3\) \(60.686\) 3.3.257.1 None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{3}+(1-\beta _{1})q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.bz \(3\) \(60.686\) 3.3.993.1 None \(0\) \(2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{3}+(1-\beta _{2})q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.ca \(3\) \(60.686\) 3.3.321.1 None \(0\) \(2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+(1+\beta _{2})q^{3}+(1-2\beta _{1}-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
7600.2.a.cb \(3\) \(60.686\) 3.3.257.1 None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
7600.2.a.cc \(3\) \(60.686\) 3.3.169.1 None \(0\) \(2\) \(0\) \(4\) \(-\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+(1+\beta _{1})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.cd \(3\) \(60.686\) 3.3.568.1 None \(0\) \(2\) \(0\) \(4\) \(-\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+(1+\beta _{1})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
7600.2.a.ce \(4\) \(60.686\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
7600.2.a.cf \(4\) \(60.686\) 4.4.11344.1 None \(0\) \(2\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q-\beta _{2}q^{3}+(1-\beta _{1})q^{7}+(2-\beta _{3})q^{9}+\cdots\)
7600.2.a.cg \(6\) \(60.686\) 6.6.253565184.1 None \(0\) \(-2\) \(0\) \(-6\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.ch \(6\) \(60.686\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{4})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.ci \(6\) \(60.686\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}+\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
7600.2.a.cj \(6\) \(60.686\) 6.6.56310016.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{3}q^{3}-\beta _{4}q^{7}+(2-\beta _{1}+\beta _{5})q^{9}+\cdots\)
7600.2.a.ck \(6\) \(60.686\) 6.6.66064384.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{5})q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.cl \(6\) \(60.686\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(2\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{4})q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7600.2.a.cm \(6\) \(60.686\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(2\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}-\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
7600.2.a.cn \(6\) \(60.686\) 6.6.253565184.1 None \(0\) \(2\) \(0\) \(6\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{1}+\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(760))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(950))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1900))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3800))\)\(^{\oplus 2}\)