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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 $19$

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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.

\(2\)\(5\)\(7\)\(11\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(8\)
\(+\)\(+\)\(+\)\(-\)$-$\(5\)
\(+\)\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(+\)\(-\)\(-\)$+$\(6\)
\(+\)\(-\)\(+\)\(+\)$-$\(5\)
\(+\)\(-\)\(+\)\(-\)$+$\(5\)
\(+\)\(-\)\(-\)\(+\)$+$\(7\)
\(+\)\(-\)\(-\)\(-\)$-$\(7\)
\(-\)\(+\)\(+\)\(+\)$-$\(6\)
\(-\)\(+\)\(+\)\(-\)$+$\(4\)
\(-\)\(+\)\(-\)\(+\)$+$\(3\)
\(-\)\(+\)\(-\)\(-\)$-$\(9\)
\(-\)\(-\)\(+\)\(+\)$+$\(6\)
\(-\)\(-\)\(+\)\(-\)$-$\(8\)
\(-\)\(-\)\(-\)\(+\)$-$\(8\)
\(-\)\(-\)\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(41\)
Minus space\(-\)\(53\)

Trace form

\( 94 q - 2 q^{2} - 4 q^{3} + 94 q^{4} - 2 q^{8} + 86 q^{9} + O(q^{10}) \) \( 94 q - 2 q^{2} - 4 q^{3} + 94 q^{4} - 2 q^{8} + 86 q^{9} - 2 q^{11} - 4 q^{12} - 12 q^{13} - 4 q^{14} + 94 q^{16} + 4 q^{17} - 18 q^{18} + 8 q^{19} + 2 q^{22} - 8 q^{23} + 32 q^{26} - 16 q^{27} + 28 q^{29} - 8 q^{31} - 2 q^{32} - 4 q^{33} + 20 q^{34} + 86 q^{36} - 12 q^{37} + 12 q^{38} - 40 q^{39} + 12 q^{41} + 4 q^{42} + 8 q^{43} - 2 q^{44} + 16 q^{46} - 24 q^{47} - 4 q^{48} + 94 q^{49} - 48 q^{51} - 12 q^{52} + 28 q^{53} + 24 q^{54} - 4 q^{56} - 8 q^{57} + 4 q^{58} - 36 q^{59} + 12 q^{61} + 40 q^{62} + 8 q^{63} + 94 q^{64} + 24 q^{67} + 4 q^{68} + 64 q^{69} + 72 q^{71} - 18 q^{72} - 12 q^{73} + 28 q^{74} + 8 q^{76} + 4 q^{77} + 40 q^{78} - 32 q^{79} + 142 q^{81} - 20 q^{82} + 32 q^{83} - 8 q^{86} - 16 q^{87} + 2 q^{88} + 84 q^{89} + 4 q^{91} - 8 q^{92} + 24 q^{93} + 40 q^{94} - 28 q^{97} - 2 q^{98} + 54 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3850))\) 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 5 7 11
3850.2.a.a 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.b 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.c 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.d 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.e 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}+q^{11}+\cdots\)
3850.2.a.f 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.g 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.h 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.i 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.j 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.k 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.l 3850.a 1.a $1$ $30.742$ \(\Q\) None \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.m 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(-2\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.n 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(-2\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.o 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(-2\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.p 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.q 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.r 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.s 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.t 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.u 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.v 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.w 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.x 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-q^{11}+\cdots\)
3850.2.a.y 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}+q^{11}+\cdots\)
3850.2.a.z 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.ba 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(2\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.bb 3850.a 1.a $1$ $30.742$ \(\Q\) None \(1\) \(2\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.bc 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{33}) \) None \(-2\) \(-4\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.bd 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots\)
3850.2.a.be 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.bf 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
3850.2.a.bg 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+q^{7}-q^{8}+\cdots\)
3850.2.a.bh 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+q^{7}-q^{8}+\cdots\)
3850.2.a.bi 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+q^{7}-q^{8}+\cdots\)
3850.2.a.bj 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
3850.2.a.bk 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
3850.2.a.bl 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
3850.2.a.bm 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
3850.2.a.bn 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.bo 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-q^{7}+q^{8}+\cdots\)
3850.2.a.bp 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.bq 3850.a 1.a $2$ $30.742$ \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
3850.2.a.br 3850.a 1.a $3$ $30.742$ 3.3.940.1 None \(-3\) \(-3\) \(0\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
3850.2.a.bs 3850.a 1.a $3$ $30.742$ 3.3.316.1 None \(-3\) \(-2\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
3850.2.a.bt 3850.a 1.a $3$ $30.742$ 3.3.316.1 None \(-3\) \(-2\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)
3850.2.a.bu 3850.a 1.a $3$ $30.742$ 3.3.892.1 None \(3\) \(0\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{7}+\cdots\)
3850.2.a.bv 3850.a 1.a $3$ $30.742$ 3.3.316.1 None \(3\) \(2\) \(0\) \(-3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
3850.2.a.bw 3850.a 1.a $3$ $30.742$ 3.3.940.1 None \(3\) \(3\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
3850.2.a.bx 3850.a 1.a $4$ $30.742$ 4.4.10304.1 None \(-4\) \(0\) \(0\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+q^{7}+\cdots\)
3850.2.a.by 3850.a 1.a $4$ $30.742$ 4.4.10304.1 None \(4\) \(0\) \(0\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}-q^{7}+\cdots\)
3850.2.a.bz 3850.a 1.a $5$ $30.742$ 5.5.117688.1 None \(-5\) \(0\) \(0\) \(5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+q^{7}+\cdots\)
3850.2.a.ca 3850.a 1.a $5$ $30.742$ 5.5.117688.1 None \(5\) \(0\) \(0\) \(-5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}-q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(\Gamma_0(3850)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1925))\)\(^{\oplus 2}\)