Properties

Label 9200.2.a
Level $9200$
Weight $2$
Character orbit 9200.a
Rep. character $\chi_{9200}(1,\cdot)$
Character field $\Q$
Dimension $209$
Newform subspaces $83$
Sturm bound $2880$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 83 \)
Sturm bound: \(2880\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9200))\).

Total New Old
Modular forms 1476 209 1267
Cusp forms 1405 209 1196
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.

\(2\)\(5\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(25\)
\(+\)\(+\)\(-\)\(-\)\(25\)
\(+\)\(-\)\(+\)\(-\)\(27\)
\(+\)\(-\)\(-\)\(+\)\(27\)
\(-\)\(+\)\(+\)\(-\)\(29\)
\(-\)\(+\)\(-\)\(+\)\(20\)
\(-\)\(-\)\(+\)\(+\)\(25\)
\(-\)\(-\)\(-\)\(-\)\(31\)
Plus space\(+\)\(97\)
Minus space\(-\)\(112\)

Trace form

\( 209q + 2q^{3} + 4q^{7} + 205q^{9} + O(q^{10}) \) \( 209q + 2q^{3} + 4q^{7} + 205q^{9} + 2q^{13} - 6q^{17} + 4q^{19} - 3q^{23} + 2q^{27} + 2q^{29} + 22q^{31} + 8q^{33} + 10q^{37} - 18q^{39} + 2q^{41} + 32q^{43} + 2q^{47} + 225q^{49} - 44q^{51} - 6q^{53} + 8q^{57} - 8q^{59} + 2q^{61} - 40q^{63} + 16q^{67} + 6q^{71} - 6q^{73} - 8q^{77} + 52q^{79} + 201q^{81} - 20q^{83} + 10q^{87} - 14q^{89} + 60q^{91} + 12q^{93} - 14q^{97} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9200))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 23
9200.2.a.a \(1\) \(73.462\) \(\Q\) None \(0\) \(-3\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q-3q^{3}-4q^{7}+6q^{9}-3q^{11}-6q^{13}+\cdots\)
9200.2.a.b \(1\) \(73.462\) \(\Q\) None \(0\) \(-3\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q-3q^{3}-4q^{7}+6q^{9}-2q^{11}+5q^{13}+\cdots\)
9200.2.a.c \(1\) \(73.462\) \(\Q\) None \(0\) \(-3\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q-3q^{3}-2q^{7}+6q^{9}-q^{13}+6q^{21}+\cdots\)
9200.2.a.d \(1\) \(73.462\) \(\Q\) None \(0\) \(-2\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(q-2q^{3}-3q^{7}+q^{9}+6q^{13}+7q^{17}+\cdots\)
9200.2.a.e \(1\) \(73.462\) \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(q-2q^{3}-q^{7}+q^{9}-5q^{11}+7q^{13}+\cdots\)
9200.2.a.f \(1\) \(73.462\) \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q-2q^{3}-q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
9200.2.a.g \(1\) \(73.462\) \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(q-2q^{3}-q^{7}+q^{9}+2q^{13}-5q^{17}+\cdots\)
9200.2.a.h \(1\) \(73.462\) \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-2q^{3}-q^{7}+q^{9}+3q^{11}-5q^{13}+\cdots\)
9200.2.a.i \(1\) \(73.462\) \(\Q\) None \(0\) \(-2\) \(0\) \(1\) \(+\) \(-\) \(+\) \(q-2q^{3}+q^{7}+q^{9}+5q^{11}-q^{13}+\cdots\)
9200.2.a.j \(1\) \(73.462\) \(\Q\) None \(0\) \(-2\) \(0\) \(3\) \(+\) \(-\) \(-\) \(q-2q^{3}+3q^{7}+q^{9}-5q^{11}-5q^{13}+\cdots\)
9200.2.a.k \(1\) \(73.462\) \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(q-q^{3}-4q^{7}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
9200.2.a.l \(1\) \(73.462\) \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q-q^{3}-4q^{7}-2q^{9}+2q^{11}-7q^{13}+\cdots\)
9200.2.a.m \(1\) \(73.462\) \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{7}-2q^{9}+4q^{11}-q^{13}+\cdots\)
9200.2.a.n \(1\) \(73.462\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{9}-2q^{11}+5q^{13}+4q^{17}+\cdots\)
9200.2.a.o \(1\) \(73.462\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q-q^{3}+2q^{7}-2q^{9}+4q^{11}+5q^{13}+\cdots\)
9200.2.a.p \(1\) \(73.462\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q-4q^{7}-3q^{9}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
9200.2.a.q \(1\) \(73.462\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{7}-3q^{9}-6q^{11}-6q^{13}-7q^{17}+\cdots\)
9200.2.a.r \(1\) \(73.462\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{7}-3q^{9}+q^{11}+q^{13}+5q^{19}+\cdots\)
9200.2.a.s \(1\) \(73.462\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{7}-3q^{9}+3q^{11}+3q^{13}+8q^{17}+\cdots\)
9200.2.a.t \(1\) \(73.462\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+q^{7}-3q^{9}-2q^{11}+2q^{13}-3q^{17}+\cdots\)
9200.2.a.u \(1\) \(73.462\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+q^{7}-3q^{9}+q^{11}-q^{13}+5q^{19}+\cdots\)
9200.2.a.v \(1\) \(73.462\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+q^{7}-3q^{9}+3q^{11}-3q^{13}-8q^{17}+\cdots\)
9200.2.a.w \(1\) \(73.462\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q+q^{7}-3q^{9}+6q^{11}+2q^{13}+3q^{17}+\cdots\)
9200.2.a.x \(1\) \(73.462\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+4q^{7}-3q^{9}-6q^{11}+2q^{13}-6q^{17}+\cdots\)
9200.2.a.y \(1\) \(73.462\) \(\Q\) None \(0\) \(1\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{3}-4q^{7}-2q^{9}+6q^{11}+q^{13}+\cdots\)
9200.2.a.z \(1\) \(73.462\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q+q^{3}-2q^{7}-2q^{9}-q^{13}+4q^{17}+\cdots\)
9200.2.a.ba \(1\) \(73.462\) \(\Q\) None \(0\) \(1\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+q^{3}+2q^{7}-2q^{9}+q^{13}+6q^{17}+\cdots\)
9200.2.a.bb \(1\) \(73.462\) \(\Q\) None \(0\) \(1\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+q^{3}+4q^{7}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
9200.2.a.bc \(1\) \(73.462\) \(\Q\) None \(0\) \(2\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(q+2q^{3}-3q^{7}+q^{9}-5q^{11}+5q^{13}+\cdots\)
9200.2.a.bd \(1\) \(73.462\) \(\Q\) None \(0\) \(2\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(q+2q^{3}-q^{7}+q^{9}+5q^{11}+q^{13}+\cdots\)
9200.2.a.be \(1\) \(73.462\) \(\Q\) None \(0\) \(2\) \(0\) \(1\) \(-\) \(+\) \(+\) \(q+2q^{3}+q^{7}+q^{9}-5q^{11}-7q^{13}+\cdots\)
9200.2.a.bf \(1\) \(73.462\) \(\Q\) None \(0\) \(2\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q+2q^{3}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
9200.2.a.bg \(1\) \(73.462\) \(\Q\) None \(0\) \(2\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q+2q^{3}+q^{7}+q^{9}-2q^{13}+5q^{17}+\cdots\)
9200.2.a.bh \(1\) \(73.462\) \(\Q\) None \(0\) \(2\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+2q^{3}+q^{7}+q^{9}+3q^{11}+5q^{13}+\cdots\)
9200.2.a.bi \(1\) \(73.462\) \(\Q\) None \(0\) \(2\) \(0\) \(3\) \(+\) \(-\) \(-\) \(q+2q^{3}+3q^{7}+q^{9}-6q^{13}-7q^{17}+\cdots\)
9200.2.a.bj \(1\) \(73.462\) \(\Q\) None \(0\) \(3\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q+3q^{3}-2q^{7}+6q^{9}+5q^{13}+6q^{17}+\cdots\)
9200.2.a.bk \(1\) \(73.462\) \(\Q\) None \(0\) \(3\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+3q^{3}+2q^{7}+6q^{9}+3q^{13}-4q^{17}+\cdots\)
9200.2.a.bl \(1\) \(73.462\) \(\Q\) None \(0\) \(3\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+3q^{3}+4q^{7}+6q^{9}-3q^{11}+6q^{13}+\cdots\)
9200.2.a.bm \(2\) \(73.462\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-q^{3}+(-1+\beta )q^{7}-2q^{9}+(1+\beta )q^{11}+\cdots\)
9200.2.a.bn \(2\) \(73.462\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(4\) \(+\) \(-\) \(-\) \(q+(-1-\beta )q^{3}+(2+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
9200.2.a.bo \(2\) \(73.462\) \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(q-\beta q^{3}+(-3+3\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
9200.2.a.bp \(2\) \(73.462\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
9200.2.a.bq \(2\) \(73.462\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+2q^{11}+\cdots\)
9200.2.a.br \(2\) \(73.462\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-\beta q^{3}+(1+\beta )q^{9}-2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9200.2.a.bs \(2\) \(73.462\) \(\Q(\sqrt{21}) \) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q-\beta q^{3}+(1-\beta )q^{7}+(2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
9200.2.a.bt \(2\) \(73.462\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q-\beta q^{3}+(1+\beta )q^{7}+2q^{9}+(3+\beta )q^{11}+\cdots\)
9200.2.a.bu \(2\) \(73.462\) \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
9200.2.a.bv \(2\) \(73.462\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+\beta q^{3}+(1-\beta )q^{7}+(1+\beta )q^{9}-2q^{11}+\cdots\)
9200.2.a.bw \(2\) \(73.462\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+\beta q^{3}+(1-\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
9200.2.a.bx \(2\) \(73.462\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{3}+2\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots\)
9200.2.a.by \(2\) \(73.462\) \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(0\) \(3\) \(-\) \(-\) \(-\) \(q+\beta q^{3}+(3-3\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
9200.2.a.bz \(2\) \(73.462\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q+(1+\beta )q^{3}+(-2-\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
9200.2.a.ca \(2\) \(73.462\) \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(0\) \(3\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{3}+(2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
9200.2.a.cb \(3\) \(73.462\) \(\Q(\zeta_{14})^+\) None \(0\) \(-2\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q+(-1-\beta _{2})q^{3}+(-2-2\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
9200.2.a.cc \(3\) \(73.462\) 3.3.321.1 None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{3}-2\beta _{1}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cd \(3\) \(73.462\) 3.3.621.1 None \(0\) \(0\) \(0\) \(3\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}+(1+\beta _{1})q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
9200.2.a.ce \(3\) \(73.462\) 3.3.2597.1 None \(0\) \(1\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}+(1-\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
9200.2.a.cf \(3\) \(73.462\) 3.3.1101.1 None \(0\) \(1\) \(0\) \(3\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cg \(3\) \(73.462\) 3.3.321.1 None \(0\) \(2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{3}+2\beta _{1}q^{7}+(1-\beta _{1}+\beta _{2})q^{9}+\cdots\)
9200.2.a.ch \(3\) \(73.462\) \(\Q(\zeta_{14})^+\) None \(0\) \(2\) \(0\) \(4\) \(+\) \(+\) \(+\) \(q+(1-\beta _{1})q^{3}+(2-2\beta _{1})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.ci \(3\) \(73.462\) 3.3.229.1 None \(0\) \(2\) \(0\) \(7\) \(+\) \(+\) \(+\) \(q+(1+\beta _{2})q^{3}+(2-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cj \(4\) \(73.462\) 4.4.13448.1 None \(0\) \(-3\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{3})q^{3}+(-1-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
9200.2.a.ck \(4\) \(73.462\) 4.4.5744.1 None \(0\) \(-2\) \(0\) \(-6\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{3}+(-2-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
9200.2.a.cl \(4\) \(73.462\) 4.4.15317.1 None \(0\) \(-2\) \(0\) \(-3\) \(-\) \(+\) \(+\) \(q+(-1-\beta _{2})q^{3}+(-1-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
9200.2.a.cm \(4\) \(73.462\) 4.4.53121.1 None \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
9200.2.a.cn \(4\) \(73.462\) 4.4.15529.1 None \(0\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.co \(4\) \(73.462\) 4.4.53121.1 None \(0\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9200.2.a.cp \(4\) \(73.462\) 4.4.15529.1 None \(0\) \(0\) \(0\) \(1\) \(+\) \(-\) \(+\) \(q-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(2-2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
9200.2.a.cq \(4\) \(73.462\) 4.4.5744.1 None \(0\) \(2\) \(0\) \(6\) \(-\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+(2+\beta _{2})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cr \(4\) \(73.462\) 4.4.13448.1 None \(0\) \(3\) \(0\) \(3\) \(-\) \(-\) \(-\) \(q+(1+\beta _{2})q^{3}+(1+\beta _{3})q^{7}+(2+2\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cs \(5\) \(73.462\) 5.5.791953.1 None \(0\) \(-3\) \(0\) \(1\) \(+\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4})q^{7}+\cdots\)
9200.2.a.ct \(5\) \(73.462\) 5.5.521397.1 None \(0\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9200.2.a.cu \(5\) \(73.462\) 5.5.13955077.1 None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(-\beta _{3}-\beta _{4})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9200.2.a.cv \(5\) \(73.462\) 5.5.521397.1 None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9200.2.a.cw \(5\) \(73.462\) 5.5.791953.1 None \(0\) \(3\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(q+(1-\beta _{1})q^{3}+(-1+\beta _{2}-\beta _{4})q^{7}+\cdots\)
9200.2.a.cx \(6\) \(73.462\) 6.6.143376304.1 None \(0\) \(-4\) \(0\) \(-9\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{3}+(-2+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
9200.2.a.cy \(6\) \(73.462\) 6.6.143376304.1 None \(0\) \(4\) \(0\) \(9\) \(-\) \(-\) \(-\) \(q+(1+\beta _{2})q^{3}+(2-\beta _{3})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cz \(7\) \(73.462\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-3\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.da \(7\) \(73.462\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(0\) \(-3\) \(-\) \(-\) \(-\) \(q-\beta _{3}q^{3}+\beta _{2}q^{7}+(1+\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.db \(7\) \(73.462\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(0\) \(3\) \(-\) \(+\) \(+\) \(q+\beta _{3}q^{3}-\beta _{2}q^{7}+(1+\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.dc \(7\) \(73.462\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(3\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(\beta _{2}+\beta _{5}+\beta _{6})q^{9}+\cdots\)
9200.2.a.dd \(8\) \(73.462\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-3\) \(0\) \(-7\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-1-\beta _{7})q^{7}+(2+\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.de \(8\) \(73.462\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(3\) \(0\) \(7\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{7})q^{7}+(2+\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4600))\)\(^{\oplus 2}\)