↑

Properties

Label 4830.2.a
Level $4830$
Weight $2$
Character orbit 4830.a
Rep. character $\chi_{4830}(1,\cdot)$
Character field $\Q$
Dimension $87$
Newform subspaces $57$
Sturm bound $2304$
Trace bound $17$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4830.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 57 \)
Sturm bound: \(2304\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4830))\).

Total New Old
Modular forms 1168 87 1081
Cusp forms 1137 87 1050
Eisenstein series 31 0 31

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

\(2\)\(3\)\(5\)\(7\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(+\)\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(+\)\(+\)\(-\)\(-\)$+$\(1\)
\(+\)\(+\)\(-\)\(+\)\(+\)$-$\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)$+$\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)$+$\(2\)
\(+\)\(+\)\(-\)\(-\)\(-\)$-$\(3\)
\(+\)\(-\)\(+\)\(+\)\(+\)$-$\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)$+$\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)$+$\(3\)
\(+\)\(-\)\(+\)\(-\)\(-\)$-$\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)$+$\(3\)
\(+\)\(-\)\(-\)\(+\)\(-\)$-$\(3\)
\(+\)\(-\)\(-\)\(-\)\(+\)$-$\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)\(+\)\(+\)$-$\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)$+$\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)$+$\(2\)
\(-\)\(+\)\(+\)\(-\)\(-\)$-$\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)$+$\(4\)
\(-\)\(+\)\(-\)\(+\)\(-\)$-$\(2\)
\(-\)\(+\)\(-\)\(-\)\(+\)$-$\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)$+$\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)$+$\(4\)
\(-\)\(-\)\(+\)\(+\)\(-\)$-$\(3\)
\(-\)\(-\)\(+\)\(-\)\(+\)$-$\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)$+$\(1\)
\(-\)\(-\)\(-\)\(+\)\(+\)$-$\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(-\)\(-\)\(+\)$+$\(1\)
\(-\)\(-\)\(-\)\(-\)\(-\)$-$\(5\)
Plus space\(+\)\(36\)
Minus space\(-\)\(51\)

Trace form

\( 87 q - q^{2} - q^{3} + 87 q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + 87 q^{9} + O(q^{10}) \) \( 87 q - q^{2} - q^{3} + 87 q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + 87 q^{9} - q^{10} - 12 q^{11} - q^{12} - 14 q^{13} - q^{14} - q^{15} + 87 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - q^{20} - q^{21} - 12 q^{22} - q^{23} - q^{24} + 87 q^{25} - 14 q^{26} - q^{27} - q^{28} - 30 q^{29} - q^{30} - q^{32} + 20 q^{33} - 18 q^{34} - q^{35} + 87 q^{36} - 6 q^{37} - 20 q^{38} - 14 q^{39} - q^{40} - 10 q^{41} - q^{42} + 20 q^{43} - 12 q^{44} - q^{45} - q^{46} - 16 q^{47} - q^{48} + 87 q^{49} - q^{50} + 14 q^{51} - 14 q^{52} - 22 q^{53} - q^{54} - 12 q^{55} - q^{56} - 20 q^{57} - 14 q^{58} - 28 q^{59} - q^{60} + 2 q^{61} - q^{63} + 87 q^{64} - 14 q^{65} - 12 q^{66} - 36 q^{67} - 18 q^{68} - q^{69} + 7 q^{70} - 24 q^{71} - q^{72} - 42 q^{73} + 10 q^{74} - q^{75} - 20 q^{76} - 12 q^{77} + 2 q^{78} - 32 q^{79} - q^{80} + 87 q^{81} - 10 q^{82} - 20 q^{83} - q^{84} - 2 q^{85} + 4 q^{86} + 34 q^{87} - 12 q^{88} - 58 q^{89} - q^{90} - 14 q^{91} - q^{92} - 16 q^{93} + 80 q^{94} - 4 q^{95} - q^{96} - 34 q^{97} - q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4830))\) 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 7 23
4830.2.a.a 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.b 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.c 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.d 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.e 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.f 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) $+$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.g 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) $+$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.h 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.i 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.j 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.k 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.l 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.m 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.n 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.o 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.p 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.q 4830.a 1.a $1$ $38.568$ \(\Q\) None \(-1\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.r 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.s 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.t 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.u 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.v 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.w 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.x 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.y 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.z 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.ba 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bb 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bc 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bd 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.be 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bf 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bg 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bh 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bi 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bj 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bk 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bl 4830.a 1.a $1$ $38.568$ \(\Q\) None \(1\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bm 4830.a 1.a $2$ $38.568$ \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(2\) \(-2\) $+$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bn 4830.a 1.a $2$ $38.568$ \(\Q(\sqrt{13}) \) None \(-2\) \(2\) \(-2\) \(-2\) $+$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.bo 4830.a 1.a $2$ $38.568$ \(\Q(\sqrt{13}) \) None \(-2\) \(2\) \(-2\) \(2\) $+$ $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.bp 4830.a 1.a $2$ $38.568$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-2\) \(2\) $+$ $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.bq 4830.a 1.a $2$ $38.568$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(-2\) $+$ $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.br 4830.a 1.a $2$ $38.568$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(2\) \(-2\) $+$ $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.bs 4830.a 1.a $2$ $38.568$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(2\) $+$ $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.bt 4830.a 1.a $2$ $38.568$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(-2\) $-$ $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.bu 4830.a 1.a $2$ $38.568$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-2\) \(-2\) $-$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.bv 4830.a 1.a $2$ $38.568$ \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(-2\) \(-2\) $-$ $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bw 4830.a 1.a $3$ $38.568$ 3.3.316.1 None \(-3\) \(-3\) \(-3\) \(-3\) $+$ $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.bx 4830.a 1.a $3$ $38.568$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(3\) \(-3\) $+$ $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.by 4830.a 1.a $3$ $38.568$ 3.3.148.1 None \(-3\) \(-3\) \(3\) \(3\) $+$ $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.bz 4830.a 1.a $3$ $38.568$ 3.3.148.1 None \(3\) \(-3\) \(-3\) \(3\) $-$ $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.ca 4830.a 1.a $3$ $38.568$ 3.3.316.1 None \(3\) \(-3\) \(3\) \(-3\) $-$ $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
4830.2.a.cb 4830.a 1.a $3$ $38.568$ 3.3.229.1 None \(3\) \(-3\) \(3\) \(3\) $-$ $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4830.2.a.cc 4830.a 1.a $3$ $38.568$ \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(-3\) \(-3\) $-$ $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
4830.2.a.cd 4830.a 1.a $4$ $38.568$ 4.4.10273.1 None \(-4\) \(-4\) \(-4\) \(4\) $+$ $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
4830.2.a.ce 4830.a 1.a $4$ $38.568$ 4.4.6809.1 None \(4\) \(4\) \(4\) \(4\) $-$ $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4830))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4830)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(805))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1610))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2415))\)\(^{\oplus 2}\)