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Properties

Label 4998.2.a
Level $4998$
Weight $2$
Character orbit 4998.a
Rep. character $\chi_{4998}(1,\cdot)$
Character field $\Q$
Dimension $108$
Newform subspaces $68$
Sturm bound $2016$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4998.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 68 \)
Sturm bound: \(2016\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4998))\).

Total New Old
Modular forms 1040 108 932
Cusp forms 977 108 869
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.

\(2\)\(3\)\(7\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(8\)
\(+\)\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(+\)\(-\)\(-\)$+$\(8\)
\(+\)\(-\)\(+\)\(+\)$-$\(7\)
\(+\)\(-\)\(+\)\(-\)$+$\(5\)
\(+\)\(-\)\(-\)\(+\)$+$\(6\)
\(+\)\(-\)\(-\)\(-\)$-$\(9\)
\(-\)\(+\)\(+\)\(+\)$-$\(7\)
\(-\)\(+\)\(+\)\(-\)$+$\(5\)
\(-\)\(+\)\(-\)\(+\)$+$\(8\)
\(-\)\(+\)\(-\)\(-\)$-$\(8\)
\(-\)\(-\)\(+\)\(+\)$+$\(4\)
\(-\)\(-\)\(+\)\(-\)$-$\(10\)
\(-\)\(-\)\(-\)\(+\)$-$\(9\)
\(-\)\(-\)\(-\)\(-\)$+$\(3\)
Plus space\(+\)\(47\)
Minus space\(-\)\(61\)

Trace form

\( 108 q - 2 q^{3} + 108 q^{4} - 2 q^{6} + 108 q^{9} + O(q^{10}) \) \( 108 q - 2 q^{3} + 108 q^{4} - 2 q^{6} + 108 q^{9} - 8 q^{10} - 8 q^{11} - 2 q^{12} + 108 q^{16} - 16 q^{19} - 8 q^{23} - 2 q^{24} + 84 q^{25} - 2 q^{27} - 16 q^{29} - 8 q^{31} - 4 q^{34} + 108 q^{36} + 24 q^{37} + 8 q^{38} + 36 q^{39} - 8 q^{40} - 16 q^{41} + 32 q^{43} - 8 q^{44} + 8 q^{46} - 2 q^{48} + 8 q^{50} + 2 q^{51} + 16 q^{53} - 2 q^{54} + 16 q^{55} + 48 q^{57} + 16 q^{58} + 24 q^{59} + 8 q^{61} + 8 q^{62} + 108 q^{64} - 32 q^{65} + 8 q^{66} + 56 q^{67} + 12 q^{69} + 24 q^{71} + 8 q^{73} - 16 q^{74} - 14 q^{75} - 16 q^{76} + 4 q^{78} + 48 q^{79} + 108 q^{81} + 8 q^{82} - 8 q^{83} + 8 q^{85} - 16 q^{86} + 16 q^{87} - 8 q^{90} - 8 q^{92} + 36 q^{93} + 16 q^{94} + 32 q^{95} - 2 q^{96} - 8 q^{97} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4998))\) 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 7 17
4998.2.a.a 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.b 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.c 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.d 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
4998.2.a.e 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.f 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.g 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.h 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.i 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.j 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.k 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(-3\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.l 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.m 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.n 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.o 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.p 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.q 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.r 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.s 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.t 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.u 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.v 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.w 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(3\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.x 4998.a 1.a $1$ $39.909$ \(\Q\) None \(-1\) \(1\) \(4\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.y 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.z 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.ba 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bb 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bc 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bd 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.be 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bf 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(-1\) \(3\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bg 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(-1\) \(3\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bh 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(1\) \(-3\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bi 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(1\) \(-3\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bj 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(1\) \(-3\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bk 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bl 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bm 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bn 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bo 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bp 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bq 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.br 4998.a 1.a $1$ $39.909$ \(\Q\) None \(1\) \(1\) \(3\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bs 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{41}) \) None \(-2\) \(-2\) \(-1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.bt 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
4998.2.a.bu 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(3\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
4998.2.a.bv 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
4998.2.a.bw 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{6}) \) None \(2\) \(-2\) \(-4\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bx 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
4998.2.a.by 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{57}) \) None \(2\) \(-2\) \(-2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bz 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1-2\beta )q^{5}-q^{6}+\cdots\)
4998.2.a.ca 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2\beta q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.cb 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.cc 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.cd 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1-2\beta )q^{5}+q^{6}+\cdots\)
4998.2.a.ce 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2\beta q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.cf 4998.a 1.a $2$ $39.909$ \(\Q(\sqrt{57}) \) None \(2\) \(2\) \(2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.cg 4998.a 1.a $3$ $39.909$ 3.3.1944.1 None \(-3\) \(-3\) \(-3\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta _{2})q^{5}+q^{6}+\cdots\)
4998.2.a.ch 4998.a 1.a $3$ $39.909$ 3.3.1944.1 None \(-3\) \(3\) \(3\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{2})q^{5}-q^{6}+\cdots\)
4998.2.a.ci 4998.a 1.a $3$ $39.909$ 3.3.469.1 None \(3\) \(-3\) \(-1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.cj 4998.a 1.a $3$ $39.909$ 3.3.469.1 None \(3\) \(3\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.ck 4998.a 1.a $4$ $39.909$ 4.4.10304.1 None \(-4\) \(-4\) \(-2\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
4998.2.a.cl 4998.a 1.a $4$ $39.909$ 4.4.31808.1 None \(-4\) \(-4\) \(2\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.cm 4998.a 1.a $4$ $39.909$ 4.4.31808.1 None \(-4\) \(4\) \(-2\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
4998.2.a.cn 4998.a 1.a $4$ $39.909$ 4.4.10304.1 None \(-4\) \(4\) \(2\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
4998.2.a.co 4998.a 1.a $4$ $39.909$ 4.4.16448.2 None \(4\) \(-4\) \(-2\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
4998.2.a.cp 4998.a 1.a $4$ $39.909$ 4.4.16448.2 None \(4\) \(4\) \(2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4998))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4998)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(714))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(833))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1666))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2499))\)\(^{\oplus 2}\)