Properties

Label 3850.2.a
Level $3850$
Weight $2$
Character orbit 3850.a
Rep. character $\chi_{3850}(1,\cdot)$
Character field $\Q$
Dimension $94$
Newform subspaces $53$
Sturm bound $1440$
Trace bound $19$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3850.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 53 \)
Sturm bound: \(1440\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3850))\).

Total New Old
Modular forms 744 94 650
Cusp forms 697 94 603
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.

\(2\)\(5\)\(7\)\(11\)FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(+\)\(+\)\(+\)\(+\)\(42\)\(8\)\(34\)\(40\)\(8\)\(32\)\(2\)\(0\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(48\)\(5\)\(43\)\(45\)\(5\)\(40\)\(3\)\(0\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(51\)\(5\)\(46\)\(48\)\(5\)\(43\)\(3\)\(0\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(45\)\(6\)\(39\)\(42\)\(6\)\(36\)\(3\)\(0\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(50\)\(5\)\(45\)\(47\)\(5\)\(42\)\(3\)\(0\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(46\)\(5\)\(41\)\(43\)\(5\)\(38\)\(3\)\(0\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(43\)\(7\)\(36\)\(40\)\(7\)\(33\)\(3\)\(0\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(47\)\(7\)\(40\)\(44\)\(7\)\(37\)\(3\)\(0\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(45\)\(6\)\(39\)\(42\)\(6\)\(36\)\(3\)\(0\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(45\)\(4\)\(41\)\(42\)\(4\)\(38\)\(3\)\(0\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(48\)\(3\)\(45\)\(45\)\(3\)\(42\)\(3\)\(0\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(48\)\(9\)\(39\)\(45\)\(9\)\(36\)\(3\)\(0\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(49\)\(6\)\(43\)\(46\)\(6\)\(40\)\(3\)\(0\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(47\)\(8\)\(39\)\(44\)\(8\)\(36\)\(3\)\(0\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(44\)\(8\)\(36\)\(41\)\(8\)\(33\)\(3\)\(0\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(46\)\(2\)\(44\)\(43\)\(2\)\(41\)\(3\)\(0\)\(3\)
Plus space\(+\)\(364\)\(41\)\(323\)\(341\)\(41\)\(300\)\(23\)\(0\)\(23\)
Minus space\(-\)\(380\)\(53\)\(327\)\(356\)\(53\)\(303\)\(24\)\(0\)\(24\)

Trace form

\( 94 q - 2 q^{2} - 4 q^{3} + 94 q^{4} - 2 q^{8} + 86 q^{9} - 2 q^{11} - 4 q^{12} - 12 q^{13} - 4 q^{14} + 94 q^{16} + 4 q^{17} - 18 q^{18} + 8 q^{19} + 2 q^{22} - 8 q^{23} + 32 q^{26} - 16 q^{27} + 28 q^{29}+ \cdots + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3850))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 7 11
3850.2.a.a 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.a \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.b 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.c.c \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.c 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.c \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.d 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.c.a \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.e 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.c.b \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}+q^{11}+\cdots\)
3850.2.a.f 3850.a 1.a $1$ $30.742$ \(\Q\) None 154.2.a.c \(-1\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.g 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.g \(-1\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.h 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.h \(-1\) \(1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.i 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.i \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.j 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.a.g \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.k 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.a.f \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.l 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.l \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.m 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.a.e \(1\) \(-2\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.n 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.l \(1\) \(-2\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.o 3850.a 1.a $1$ $30.742$ \(\Q\) None 154.2.a.b \(1\) \(-2\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.p 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.h \(1\) \(-1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.q 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.i \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.r 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.g \(1\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.s 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.a.d \(1\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.t 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.a.c \(1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.u 3850.a 1.a $1$ $30.742$ \(\Q\) None 154.2.a.a \(1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.v 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.c.a \(1\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.w 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.c \(1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.x 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.c.c \(1\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.y 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.c.b \(1\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}+q^{11}+\cdots\)
3850.2.a.z 3850.a 1.a $1$ $30.742$ \(\Q\) None 3850.2.a.a \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.ba 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.a.a \(1\) \(2\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.bb 3850.a 1.a $1$ $30.742$ \(\Q\) None 770.2.a.b \(1\) \(2\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.bc 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{33}) \) None 770.2.a.k \(-2\) \(-4\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.bd 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None 770.2.a.j \(-2\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots\)
3850.2.a.be 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{6}) \) None 770.2.c.d \(-2\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.bf 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{10}) \) None 3850.2.a.bf \(-2\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.bg 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{2}) \) None 3850.2.a.bg \(-2\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+q^{7}-q^{8}+\cdots\)
3850.2.a.bh 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{7}) \) None 3850.2.a.bh \(-2\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+q^{7}-q^{8}+\cdots\)
3850.2.a.bi 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{2}) \) None 770.2.a.i \(-2\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+q^{7}-q^{8}+\cdots\)
3850.2.a.bj 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{5}) \) None 154.2.a.d \(-2\) \(2\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
3850.2.a.bk 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None 3850.2.a.bk \(-2\) \(2\) \(0\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
3850.2.a.bl 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None 3850.2.a.bk \(2\) \(-2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
3850.2.a.bm 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None 770.2.a.h \(2\) \(-2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
3850.2.a.bn 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{2}) \) None 3850.2.a.bg \(2\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.bo 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{7}) \) None 3850.2.a.bh \(2\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.bp 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{6}) \) None 770.2.c.d \(2\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.bq 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{10}) \) None 3850.2.a.bf \(2\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.br 3850.a 1.a $3$ $30.742$ 3.3.940.1 None 3850.2.a.br \(-3\) \(-3\) \(0\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
3850.2.a.bs 3850.a 1.a $3$ $30.742$ 3.3.316.1 None 3850.2.a.bs \(-3\) \(-2\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
3850.2.a.bt 3850.a 1.a $3$ $30.742$ 3.3.316.1 None 770.2.a.m \(-3\) \(-2\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)
3850.2.a.bu 3850.a 1.a $3$ $30.742$ 3.3.892.1 None 770.2.a.l \(3\) \(0\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{7}+\cdots\)
3850.2.a.bv 3850.a 1.a $3$ $30.742$ 3.3.316.1 None 3850.2.a.bs \(3\) \(2\) \(0\) \(-3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
3850.2.a.bw 3850.a 1.a $3$ $30.742$ 3.3.940.1 None 3850.2.a.br \(3\) \(3\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
3850.2.a.bx 3850.a 1.a $4$ $30.742$ 4.4.10304.1 None 770.2.c.e \(-4\) \(0\) \(0\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+q^{7}+\cdots\)
3850.2.a.by 3850.a 1.a $4$ $30.742$ 4.4.10304.1 None 770.2.c.e \(4\) \(0\) \(0\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}-q^{7}+\cdots\)
3850.2.a.bz 3850.a 1.a $5$ $30.742$ 5.5.117688.1 None 770.2.c.f \(-5\) \(0\) \(0\) \(5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+q^{7}+\cdots\)
3850.2.a.ca 3850.a 1.a $5$ $30.742$ 5.5.117688.1 None 770.2.c.f \(5\) \(0\) \(0\) \(-5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}-q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3850))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3850)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1925))\)\(^{\oplus 2}\)