Properties

Label 6930.2.a
Level $6930$
Weight $2$
Character orbit 6930.a
Rep. character $\chi_{6930}(1,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $65$
Sturm bound $3456$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6930.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 65 \)
Sturm bound: \(3456\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(13\), \(17\), \(19\), \(23\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6930))\).

Total New Old
Modular forms 1760 100 1660
Cusp forms 1697 100 1597
Eisenstein series 63 0 63

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

\(2\)\(3\)\(5\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(42\)
Minus space\(-\)\(58\)

Trace form

\( 100q + 100q^{4} + O(q^{10}) \) \( 100q + 100q^{4} + 100q^{16} - 16q^{17} - 16q^{19} - 4q^{22} - 24q^{23} + 100q^{25} - 8q^{26} - 16q^{29} - 8q^{31} - 24q^{37} - 24q^{38} - 40q^{47} + 100q^{49} + 24q^{53} - 16q^{59} - 32q^{61} + 16q^{62} + 100q^{64} - 16q^{65} + 24q^{67} - 16q^{68} - 4q^{70} - 32q^{71} - 24q^{74} - 16q^{76} + 8q^{77} + 40q^{79} + 32q^{82} + 16q^{83} - 16q^{86} - 4q^{88} + 8q^{89} + 16q^{91} - 24q^{92} + 48q^{94} + 24q^{95} + 40q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6930))\) 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 7 11
6930.2.a.a \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.b \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.c \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.d \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.e \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.f \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.g \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.h \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.i \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.j \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.k \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.l \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.m \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.n \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.o \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.p \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.q \(1\) \(55.336\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.r \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.s \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.t \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.u \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.v \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.w \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.x \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.y \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.z \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.ba \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.bb \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bc \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bd \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.be \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bf \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bg \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bh \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bi \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bj \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(+\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bk \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bl \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bm \(1\) \(55.336\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.bn \(2\) \(55.336\) \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.bo \(2\) \(55.336\) \(\Q(\sqrt{33}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.bp \(2\) \(55.336\) \(\Q(\sqrt{13}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.bq \(2\) \(55.336\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.br \(2\) \(55.336\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bs \(2\) \(55.336\) \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(2\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bt \(2\) \(55.336\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bu \(2\) \(55.336\) \(\Q(\sqrt{13}) \) None \(-2\) \(0\) \(2\) \(2\) \(+\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bv \(2\) \(55.336\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.bw \(2\) \(55.336\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.bx \(2\) \(55.336\) \(\Q(\sqrt{17}) \) None \(2\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.by \(2\) \(55.336\) \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.bz \(2\) \(55.336\) \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.ca \(2\) \(55.336\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.cb \(2\) \(55.336\) \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.cc \(2\) \(55.336\) \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.cd \(2\) \(55.336\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.ce \(3\) \(55.336\) 3.3.316.1 None \(-3\) \(0\) \(-3\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.cf \(3\) \(55.336\) 3.3.316.1 None \(-3\) \(0\) \(-3\) \(-3\) \(+\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.cg \(3\) \(55.336\) \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(-3\) \(-3\) \(+\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.ch \(3\) \(55.336\) 3.3.148.1 None \(-3\) \(0\) \(-3\) \(3\) \(+\) \(-\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
6930.2.a.ci \(3\) \(55.336\) \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(3\) \(3\) \(+\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
6930.2.a.cj \(3\) \(55.336\) \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(-3\) \(3\) \(-\) \(+\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
6930.2.a.ck \(3\) \(55.336\) \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(3\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.cl \(3\) \(55.336\) 3.3.892.1 None \(3\) \(0\) \(3\) \(-3\) \(-\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
6930.2.a.cm \(3\) \(55.336\) 3.3.316.1 None \(3\) \(0\) \(3\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6930))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6930)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(990))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1386))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3465))\)\(^{\oplus 2}\)