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Properties

Label 4650.2.a
Level $4650$
Weight $2$
Character orbit 4650.a
Rep. character $\chi_{4650}(1,\cdot)$
Character field $\Q$
Dimension $94$
Newform subspaces $68$
Sturm bound $1920$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4650.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 68 \)
Sturm bound: \(1920\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4650))\).

Total New Old
Modular forms 984 94 890
Cusp forms 937 94 843
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.

\(2\)\(3\)\(5\)\(31\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(6\)
\(+\)\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(+\)\(-\)\(+\)$-$\(7\)
\(+\)\(+\)\(-\)\(-\)$+$\(5\)
\(+\)\(-\)\(+\)\(+\)$-$\(6\)
\(+\)\(-\)\(+\)\(-\)$+$\(6\)
\(+\)\(-\)\(-\)\(+\)$+$\(5\)
\(+\)\(-\)\(-\)\(-\)$-$\(7\)
\(-\)\(+\)\(+\)\(+\)$-$\(7\)
\(-\)\(+\)\(+\)\(-\)$+$\(4\)
\(-\)\(+\)\(-\)\(+\)$+$\(4\)
\(-\)\(+\)\(-\)\(-\)$-$\(8\)
\(-\)\(-\)\(+\)\(+\)$+$\(4\)
\(-\)\(-\)\(+\)\(-\)$-$\(7\)
\(-\)\(-\)\(-\)\(+\)$-$\(8\)
\(-\)\(-\)\(-\)\(-\)$+$\(4\)
Plus space\(+\)\(38\)
Minus space\(-\)\(56\)

Trace form

\( 94 q - 2 q^{2} + 94 q^{4} - 8 q^{7} - 2 q^{8} + 94 q^{9} + O(q^{10}) \) \( 94 q - 2 q^{2} + 94 q^{4} - 8 q^{7} - 2 q^{8} + 94 q^{9} - 16 q^{11} - 12 q^{13} - 8 q^{14} + 94 q^{16} - 4 q^{17} - 2 q^{18} - 12 q^{19} + 20 q^{26} - 8 q^{28} + 36 q^{29} - 2 q^{32} - 4 q^{33} + 36 q^{34} + 94 q^{36} + 12 q^{37} + 28 q^{41} + 8 q^{42} - 8 q^{43} - 16 q^{44} - 8 q^{46} + 24 q^{47} + 78 q^{49} - 20 q^{51} - 12 q^{52} - 20 q^{53} - 8 q^{56} - 16 q^{57} - 12 q^{58} - 24 q^{59} - 20 q^{61} - 8 q^{63} + 94 q^{64} - 8 q^{66} - 12 q^{67} - 4 q^{68} - 16 q^{69} + 8 q^{71} - 2 q^{72} - 12 q^{73} - 12 q^{74} - 12 q^{76} + 48 q^{77} - 12 q^{78} - 8 q^{79} + 94 q^{81} + 4 q^{82} + 48 q^{83} + 8 q^{87} + 20 q^{89} - 40 q^{91} + 2 q^{93} - 28 q^{94} + 16 q^{97} - 18 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4650))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5 31
4650.2.a.a 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-5\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-5q^{7}-q^{8}+\cdots\)
4650.2.a.b 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
4650.2.a.c 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.d 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.e 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.f 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.g 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.h 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
4650.2.a.i 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.j 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.k 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.l 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots\)
4650.2.a.m 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(-1\) \(0\) \(5\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots\)
4650.2.a.n 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
4650.2.a.o 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.p 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.q 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4650.2.a.r 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
4650.2.a.s 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
4650.2.a.t 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(1\) \(0\) \(2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.u 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(1\) \(0\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
4650.2.a.v 4650.a 1.a $1$ $37.130$ \(\Q\) None \(-1\) \(1\) \(0\) \(3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots\)
4650.2.a.w 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
4650.2.a.x 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
4650.2.a.y 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(-3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.z 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.ba 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
4650.2.a.bb 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
4650.2.a.bc 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bd 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.be 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bf 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bg 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bh 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(-1\) \(0\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bi 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(-5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-5q^{7}+q^{8}+\cdots\)
4650.2.a.bj 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(-3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.bk 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.bl 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bm 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(-2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bn 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bo 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
4650.2.a.bp 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
4650.2.a.bq 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.br 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
4650.2.a.bs 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bt 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
4650.2.a.bu 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
4650.2.a.bv 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
4650.2.a.bw 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
4650.2.a.bx 4650.a 1.a $1$ $37.130$ \(\Q\) None \(1\) \(1\) \(0\) \(5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+5q^{7}+q^{8}+\cdots\)
4650.2.a.by 4650.a 1.a $2$ $37.130$ \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-\beta q^{7}-q^{8}+\cdots\)
4650.2.a.bz 4650.a 1.a $2$ $37.130$ \(\Q(\sqrt{65}) \) None \(-2\) \(-2\) \(0\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots\)
4650.2.a.ca 4650.a 1.a $2$ $37.130$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(0\) \(4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(2+\beta )q^{7}+\cdots\)
4650.2.a.cb 4650.a 1.a $2$ $37.130$ \(\Q(\sqrt{13}) \) None \(-2\) \(-2\) \(0\) \(6\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots\)
4650.2.a.cc 4650.a 1.a $2$ $37.130$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(-4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-2+\beta )q^{7}+\cdots\)
4650.2.a.cd 4650.a 1.a $2$ $37.130$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(0\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-2\beta q^{7}-q^{8}+\cdots\)
4650.2.a.ce 4650.a 1.a $2$ $37.130$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-\beta q^{7}-q^{8}+\cdots\)
4650.2.a.cf 4650.a 1.a $2$ $37.130$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(2+\beta )q^{7}+\cdots\)
4650.2.a.cg 4650.a 1.a $2$ $37.130$ \(\Q(\sqrt{13}) \) None \(2\) \(2\) \(0\) \(-6\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
4650.2.a.ch 4650.a 1.a $2$ $37.130$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(0\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(-2-\beta )q^{7}+\cdots\)
4650.2.a.ci 4650.a 1.a $3$ $37.130$ 3.3.1708.1 None \(-3\) \(-3\) \(0\) \(-6\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
4650.2.a.cj 4650.a 1.a $3$ $37.130$ 3.3.837.1 None \(-3\) \(3\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-\beta _{2}q^{7}-q^{8}+\cdots\)
4650.2.a.ck 4650.a 1.a $3$ $37.130$ 3.3.940.1 None \(-3\) \(3\) \(0\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
4650.2.a.cl 4650.a 1.a $3$ $37.130$ 3.3.1373.1 None \(-3\) \(3\) \(0\) \(2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(1-\beta _{2})q^{7}+\cdots\)
4650.2.a.cm 4650.a 1.a $3$ $37.130$ 3.3.1373.1 None \(3\) \(-3\) \(0\) \(-2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-1+\beta _{2})q^{7}+\cdots\)
4650.2.a.cn 4650.a 1.a $3$ $37.130$ 3.3.940.1 None \(3\) \(-3\) \(0\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
4650.2.a.co 4650.a 1.a $3$ $37.130$ 3.3.837.1 None \(3\) \(-3\) \(0\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+\beta _{2}q^{7}+q^{8}+\cdots\)
4650.2.a.cp 4650.a 1.a $3$ $37.130$ 3.3.1708.1 None \(3\) \(3\) \(0\) \(6\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4650))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4650)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(775))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(930))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2325))\)\(^{\oplus 2}\)