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Properties

Label 4851.2.a
Level $4851$
Weight $2$
Character orbit 4851.a
Rep. character $\chi_{4851}(1,\cdot)$
Character field $\Q$
Dimension $172$
Newform subspaces $60$
Sturm bound $1344$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 4851 = 3^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4851.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 60 \)
Sturm bound: \(1344\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(2\), \(5\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4851))\).

Total New Old
Modular forms 704 172 532
Cusp forms 641 172 469
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.

\(3\)\(7\)\(11\)FrickeDim
\(+\)\(+\)\(+\)$+$\(19\)
\(+\)\(+\)\(-\)$-$\(19\)
\(+\)\(-\)\(+\)$-$\(16\)
\(+\)\(-\)\(-\)$+$\(16\)
\(-\)\(+\)\(+\)$-$\(28\)
\(-\)\(+\)\(-\)$+$\(20\)
\(-\)\(-\)\(+\)$+$\(24\)
\(-\)\(-\)\(-\)$-$\(30\)
Plus space\(+\)\(79\)
Minus space\(-\)\(93\)

Trace form

\( 172 q + q^{2} + 171 q^{4} + 5 q^{5} - 9 q^{8} + O(q^{10}) \) \( 172 q + q^{2} + 171 q^{4} + 5 q^{5} - 9 q^{8} - 8 q^{10} - 2 q^{11} + 10 q^{13} + 165 q^{16} + 16 q^{17} - 12 q^{20} + q^{22} + q^{23} + 185 q^{25} - 6 q^{26} + 14 q^{29} - 13 q^{31} + 3 q^{32} + 22 q^{34} - 3 q^{37} - 16 q^{38} + 30 q^{40} + 10 q^{41} - 30 q^{43} - 9 q^{44} + 14 q^{46} + 9 q^{50} + 42 q^{52} + 28 q^{53} - q^{55} + 82 q^{58} - 21 q^{59} - 10 q^{61} - 18 q^{62} + 205 q^{64} + 84 q^{65} - 19 q^{67} + 22 q^{68} - 9 q^{71} + 34 q^{73} + 88 q^{74} + 12 q^{76} - 42 q^{79} + 18 q^{80} + 58 q^{82} + 30 q^{83} + 58 q^{85} + 56 q^{86} + 15 q^{88} + 51 q^{89} + 30 q^{92} - 20 q^{94} - 32 q^{95} + 51 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4851))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 11
4851.2.a.a 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
4851.2.a.b 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
4851.2.a.c 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+q^{11}-4q^{13}+\cdots\)
4851.2.a.d 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+q^{11}-4q^{13}+\cdots\)
4851.2.a.e 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+q^{11}+4q^{13}+\cdots\)
4851.2.a.f 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+q^{11}+4q^{13}+\cdots\)
4851.2.a.g 4851.a 1.a $1$ $38.735$ \(\Q\) None \(-1\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+4q^{5}+3q^{8}-4q^{10}+\cdots\)
4851.2.a.h 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-4q^{5}-q^{11}+5q^{13}+4q^{16}+\cdots\)
4851.2.a.i 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-4q^{5}+q^{11}-5q^{13}+4q^{16}+\cdots\)
4851.2.a.j 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}+q^{11}+4q^{13}+4q^{16}+\cdots\)
4851.2.a.k 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}+q^{11}+4q^{13}+4q^{16}+\cdots\)
4851.2.a.l 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+4q^{5}-q^{11}-5q^{13}+4q^{16}+\cdots\)
4851.2.a.m 4851.a 1.a $1$ $38.735$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+4q^{5}+q^{11}+5q^{13}+4q^{16}+\cdots\)
4851.2.a.n 4851.a 1.a $1$ $38.735$ \(\Q\) None \(1\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots\)
4851.2.a.o 4851.a 1.a $1$ $38.735$ \(\Q\) None \(1\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots\)
4851.2.a.p 4851.a 1.a $1$ $38.735$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots\)
4851.2.a.q 4851.a 1.a $1$ $38.735$ \(\Q\) None \(1\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots\)
4851.2.a.r 4851.a 1.a $1$ $38.735$ \(\Q\) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{11}-5q^{13}-4q^{16}+\cdots\)
4851.2.a.s 4851.a 1.a $1$ $38.735$ \(\Q\) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{11}+5q^{13}-4q^{16}+\cdots\)
4851.2.a.t 4851.a 1.a $1$ $38.735$ \(\Q\) None \(2\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}-q^{11}+\cdots\)
4851.2.a.u 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.v 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+\beta q^{5}+3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.w 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1+2\beta )q^{8}+\cdots\)
4851.2.a.x 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+q^{5}-3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.y 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3q^{4}-2q^{5}-\beta q^{8}+2\beta q^{10}+\cdots\)
4851.2.a.z 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.ba 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{21}) \) None \(1\) \(0\) \(6\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(3+\beta )q^{4}+3q^{5}+(5+2\beta )q^{8}+\cdots\)
4851.2.a.bb 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-\beta q^{5}-3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.bc 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-\beta q^{5}-3q^{8}-\beta q^{10}+\cdots\)
4851.2.a.bd 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2q^{5}+(3+\cdots)q^{8}+\cdots\)
4851.2.a.be 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2q^{5}+(3+\cdots)q^{8}+\cdots\)
4851.2.a.bf 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+(1+4\beta )q^{8}+\cdots\)
4851.2.a.bg 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}+(1-2\beta )q^{5}+(1+\cdots)q^{8}+\cdots\)
4851.2.a.bh 4851.a 1.a $2$ $38.735$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
4851.2.a.bi 4851.a 1.a $3$ $38.735$ 3.3.229.1 None \(-2\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bj 4851.a 1.a $3$ $38.735$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(-6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-2-\beta _{2})q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.bk 4851.a 1.a $3$ $38.735$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(2+\beta _{2})q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.bl 4851.a 1.a $3$ $38.735$ 3.3.229.1 None \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
4851.2.a.bm 4851.a 1.a $3$ $38.735$ 3.3.229.1 None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
4851.2.a.bn 4851.a 1.a $3$ $38.735$ 3.3.257.1 None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bo 4851.a 1.a $3$ $38.735$ 3.3.257.1 None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bp 4851.a 1.a $3$ $38.735$ 3.3.837.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
4851.2.a.bq 4851.a 1.a $4$ $38.735$ 4.4.725.1 None \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{1})q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{8}+\cdots\)
4851.2.a.br 4851.a 1.a $4$ $38.735$ 4.4.2624.1 None \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
4851.2.a.bs 4851.a 1.a $4$ $38.735$ 4.4.2624.1 None \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bt 4851.a 1.a $4$ $38.735$ 4.4.11344.1 None \(-2\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
4851.2.a.bu 4851.a 1.a $4$ $38.735$ 4.4.11344.1 None \(-2\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
4851.2.a.bv 4851.a 1.a $4$ $38.735$ 4.4.9248.1 None \(-2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(2-\beta _{3})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
4851.2.a.bw 4851.a 1.a $4$ $38.735$ 4.4.725.1 None \(2\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{1})q^{4}-\beta _{2}q^{5}+(1+\cdots)q^{8}+\cdots\)
4851.2.a.bx 4851.a 1.a $4$ $38.735$ 4.4.2624.1 None \(2\) \(0\) \(-8\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
4851.2.a.by 4851.a 1.a $4$ $38.735$ 4.4.2624.1 None \(2\) \(0\) \(8\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
4851.2.a.bz 4851.a 1.a $5$ $38.735$ 5.5.3676752.1 None \(-2\) \(0\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
4851.2.a.ca 4851.a 1.a $5$ $38.735$ 5.5.3676752.1 None \(-2\) \(0\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
4851.2.a.cb 4851.a 1.a $6$ $38.735$ 6.6.672323328.1 None \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
4851.2.a.cc 4851.a 1.a $6$ $38.735$ 6.6.672323328.1 None \(0\) \(0\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
4851.2.a.cd 4851.a 1.a $6$ $38.735$ 6.6.672323328.1 None \(0\) \(0\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
4851.2.a.ce 4851.a 1.a $6$ $38.735$ 6.6.672323328.1 None \(0\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
4851.2.a.cf 4851.a 1.a $10$ $38.735$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(2+\beta _{2}+\beta _{8})q^{4}-\beta _{7}q^{5}+\cdots\)
4851.2.a.cg 4851.a 1.a $10$ $38.735$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{2}+(2+\beta _{9})q^{4}+\beta _{7}q^{5}+(1+\beta _{2}+\cdots)q^{8}+\cdots\)
4851.2.a.ch 4851.a 1.a $10$ $38.735$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(2+\beta _{2}+\beta _{8})q^{4}-\beta _{7}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4851))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4851)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1617))\)\(^{\oplus 2}\)