↑

Properties

Label 5550.2.a
Level $5550$
Weight $2$
Character orbit 5550.a
Rep. character $\chi_{5550}(1,\cdot)$
Character field $\Q$
Dimension $114$
Newform subspaces $68$
Sturm bound $2280$
Trace bound $17$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 5550 = 2 \cdot 3 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5550.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 68 \)
Sturm bound: \(2280\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5550))\).

Total New Old
Modular forms 1164 114 1050
Cusp forms 1117 114 1003
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.

\(2\)\(3\)\(5\)\(37\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(4\)
\(+\)\(+\)\(+\)\(-\)$-$\(10\)
\(+\)\(+\)\(-\)\(+\)$-$\(9\)
\(+\)\(+\)\(-\)\(-\)$+$\(5\)
\(+\)\(-\)\(+\)\(+\)$-$\(8\)
\(+\)\(-\)\(+\)\(-\)$+$\(5\)
\(+\)\(-\)\(-\)\(+\)$+$\(7\)
\(+\)\(-\)\(-\)\(-\)$-$\(9\)
\(-\)\(+\)\(+\)\(+\)$-$\(8\)
\(-\)\(+\)\(+\)\(-\)$+$\(5\)
\(-\)\(+\)\(-\)\(+\)$+$\(7\)
\(-\)\(+\)\(-\)\(-\)$-$\(9\)
\(-\)\(-\)\(+\)\(+\)$+$\(4\)
\(-\)\(-\)\(+\)\(-\)$-$\(10\)
\(-\)\(-\)\(-\)\(+\)$-$\(9\)
\(-\)\(-\)\(-\)\(-\)$+$\(5\)
Plus space\(+\)\(42\)
Minus space\(-\)\(72\)

Trace form

\( 114 q + 114 q^{4} - 2 q^{6} - 12 q^{7} + 114 q^{9} + O(q^{10}) \) \( 114 q + 114 q^{4} - 2 q^{6} - 12 q^{7} + 114 q^{9} + 4 q^{13} + 8 q^{14} + 114 q^{16} + 8 q^{17} - 12 q^{19} + 8 q^{22} - 8 q^{23} - 2 q^{24} + 8 q^{26} - 12 q^{28} - 8 q^{29} + 12 q^{31} - 12 q^{33} + 114 q^{36} + 2 q^{37} + 20 q^{38} + 20 q^{41} - 12 q^{43} + 12 q^{46} + 32 q^{47} + 126 q^{49} + 4 q^{51} + 4 q^{52} + 28 q^{53} - 2 q^{54} + 8 q^{56} + 4 q^{57} + 20 q^{58} + 8 q^{59} - 12 q^{61} - 12 q^{62} - 12 q^{63} + 114 q^{64} + 8 q^{68} - 8 q^{69} + 8 q^{71} - 12 q^{76} - 8 q^{78} - 36 q^{79} + 114 q^{81} + 24 q^{83} + 4 q^{86} - 28 q^{87} + 8 q^{88} - 48 q^{89} - 32 q^{91} - 8 q^{92} - 4 q^{93} - 16 q^{94} - 2 q^{96} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5550))\) 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 37
5550.2.a.a 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
5550.2.a.b 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
5550.2.a.c 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
5550.2.a.d 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
5550.2.a.e 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
5550.2.a.f 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
5550.2.a.g 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
5550.2.a.h 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
5550.2.a.i 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
5550.2.a.j 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
5550.2.a.k 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(5\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots\)
5550.2.a.l 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(-1\) \(0\) \(5\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots\)
5550.2.a.m 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
5550.2.a.n 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
5550.2.a.o 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(1\) \(0\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
5550.2.a.p 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(1\) \(0\) \(-2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
5550.2.a.q 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5550.2.a.r 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5550.2.a.s 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(1\) \(0\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
5550.2.a.t 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(1\) \(0\) \(3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots\)
5550.2.a.u 5550.a 1.a $1$ $44.317$ \(\Q\) None \(-1\) \(1\) \(0\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
5550.2.a.v 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
5550.2.a.w 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
5550.2.a.x 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
5550.2.a.y 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
5550.2.a.z 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
5550.2.a.ba 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
5550.2.a.bb 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(-1\) \(0\) \(2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
5550.2.a.bc 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(-1\) \(0\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
5550.2.a.bd 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(-1\) \(0\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots\)
5550.2.a.be 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(-5\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-5q^{7}+q^{8}+\cdots\)
5550.2.a.bf 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
5550.2.a.bg 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(-3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
5550.2.a.bh 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
5550.2.a.bi 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(-2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
5550.2.a.bj 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(-2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
5550.2.a.bk 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
5550.2.a.bl 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
5550.2.a.bm 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
5550.2.a.bn 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
5550.2.a.bo 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
5550.2.a.bp 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
5550.2.a.bq 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
5550.2.a.br 5550.a 1.a $1$ $44.317$ \(\Q\) None \(1\) \(1\) \(0\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
5550.2.a.bs 5550.a 1.a $2$ $44.317$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-1+\beta )q^{7}+\cdots\)
5550.2.a.bt 5550.a 1.a $2$ $44.317$ \(\Q(\sqrt{6}) \) None \(-2\) \(-2\) \(0\) \(-2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-1+\beta )q^{7}+\cdots\)
5550.2.a.bu 5550.a 1.a $2$ $44.317$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(0\) \(-4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
5550.2.a.bv 5550.a 1.a $2$ $44.317$ \(\Q(\sqrt{33}) \) None \(-2\) \(2\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
5550.2.a.bw 5550.a 1.a $2$ $44.317$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(0\) \(2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
5550.2.a.bx 5550.a 1.a $2$ $44.317$ \(\Q(\sqrt{113}) \) None \(2\) \(-2\) \(0\) \(-6\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-3q^{7}+q^{8}+\cdots\)
5550.2.a.by 5550.a 1.a $2$ $44.317$ \(\Q(\sqrt{33}) \) None \(2\) \(-2\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
5550.2.a.bz 5550.a 1.a $2$ $44.317$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(0\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
5550.2.a.ca 5550.a 1.a $2$ $44.317$ \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(0\) \(1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+\beta q^{7}+q^{8}+\cdots\)
5550.2.a.cb 5550.a 1.a $2$ $44.317$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots\)
5550.2.a.cc 5550.a 1.a $2$ $44.317$ \(\Q(\sqrt{6}) \) None \(2\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots\)
5550.2.a.cd 5550.a 1.a $3$ $44.317$ 3.3.993.1 None \(-3\) \(-3\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
5550.2.a.ce 5550.a 1.a $3$ $44.317$ 3.3.257.1 None \(-3\) \(3\) \(0\) \(-4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
5550.2.a.cf 5550.a 1.a $3$ $44.317$ 3.3.568.1 None \(-3\) \(3\) \(0\) \(3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
5550.2.a.cg 5550.a 1.a $3$ $44.317$ 3.3.568.1 None \(3\) \(-3\) \(0\) \(-3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
5550.2.a.ch 5550.a 1.a $3$ $44.317$ 3.3.257.1 None \(3\) \(-3\) \(0\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
5550.2.a.ci 5550.a 1.a $3$ $44.317$ 3.3.993.1 None \(3\) \(3\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
5550.2.a.cj 5550.a 1.a $4$ $44.317$ 4.4.54764.1 None \(-4\) \(-4\) \(0\) \(-4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
5550.2.a.ck 5550.a 1.a $4$ $44.317$ 4.4.358377.1 None \(-4\) \(4\) \(0\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
5550.2.a.cl 5550.a 1.a $4$ $44.317$ 4.4.30056.1 None \(-4\) \(4\) \(0\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
5550.2.a.cm 5550.a 1.a $4$ $44.317$ 4.4.30056.1 None \(4\) \(-4\) \(0\) \(-3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
5550.2.a.cn 5550.a 1.a $4$ $44.317$ 4.4.358377.1 None \(4\) \(-4\) \(0\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
5550.2.a.co 5550.a 1.a $5$ $44.317$ 5.5.60594425.1 None \(-5\) \(-5\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-\beta _{4}q^{7}-q^{8}+\cdots\)
5550.2.a.cp 5550.a 1.a $5$ $44.317$ 5.5.60594425.1 None \(5\) \(5\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+\beta _{4}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5550))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(555))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(925))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2775))\)\(^{\oplus 2}\)