Properties

Label 9025.2.a
Level $9025$
Weight $2$
Character orbit 9025.a
Rep. character $\chi_{9025}(1,\cdot)$
Character field $\Q$
Dimension $515$
Newform subspaces $74$
Sturm bound $1900$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 9025 = 5^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9025.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 74 \)
Sturm bound: \(1900\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(3\), \(7\), \(11\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9025))\).

Total New Old
Modular forms 1010 566 444
Cusp forms 891 515 376
Eisenstein series 119 51 68

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

\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(121\)
\(+\)\(-\)\(-\)\(126\)
\(-\)\(+\)\(-\)\(139\)
\(-\)\(-\)\(+\)\(129\)
Plus space\(+\)\(250\)
Minus space\(-\)\(265\)

Trace form

\( 515 q - q^{2} + 2 q^{3} + 487 q^{4} + 2 q^{7} - 9 q^{8} + 473 q^{9} + O(q^{10}) \) \( 515 q - q^{2} + 2 q^{3} + 487 q^{4} + 2 q^{7} - 9 q^{8} + 473 q^{9} + 2 q^{11} + 6 q^{13} + 439 q^{16} + 2 q^{17} - 29 q^{18} + 6 q^{21} - 12 q^{22} - 16 q^{23} - 16 q^{24} - 14 q^{26} + 8 q^{27} + 2 q^{28} + 16 q^{31} - 9 q^{32} + 6 q^{33} + 10 q^{34} + 427 q^{36} + 16 q^{37} + 52 q^{39} - 4 q^{41} + 58 q^{42} - 6 q^{43} - 10 q^{44} - 4 q^{46} - 10 q^{47} + 40 q^{48} + 389 q^{49} + 2 q^{51} + 30 q^{52} + 18 q^{53} + 50 q^{54} + 32 q^{56} + 24 q^{58} - 2 q^{59} + 24 q^{61} + 54 q^{62} - 12 q^{63} + 281 q^{64} + 86 q^{66} - 20 q^{67} + 10 q^{68} - 18 q^{71} - 65 q^{72} + 22 q^{73} + 14 q^{74} - 28 q^{77} + 24 q^{79} + 315 q^{81} + 8 q^{82} - 20 q^{83} + 56 q^{84} - 40 q^{86} - 66 q^{87} - 16 q^{88} - 2 q^{89} + 24 q^{91} + 48 q^{92} - 40 q^{93} - 24 q^{94} - 26 q^{96} + 58 q^{97} + 23 q^{98} - 30 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9025))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 19
9025.2.a.a $1$ $72.065$ \(\Q\) None \(-2\) \(0\) \(0\) \(-4\) $-$ $-$ \(q-2q^{2}+2q^{4}-4q^{7}-3q^{9}-q^{11}+\cdots\)
9025.2.a.b $1$ $72.065$ \(\Q\) None \(-2\) \(0\) \(0\) \(4\) $-$ $+$ \(q-2q^{2}+2q^{4}+4q^{7}-3q^{9}-q^{11}+\cdots\)
9025.2.a.c $1$ $72.065$ \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) $-$ $-$ \(q-q^{2}-q^{4}-2q^{7}+3q^{8}-3q^{9}-4q^{11}+\cdots\)
9025.2.a.d $1$ $72.065$ \(\Q\) None \(0\) \(-2\) \(0\) \(1\) $+$ $-$ \(q-2q^{3}-2q^{4}+q^{7}+q^{9}+3q^{11}+\cdots\)
9025.2.a.e $1$ $72.065$ \(\Q\) None \(0\) \(-2\) \(0\) \(4\) $+$ $-$ \(q-2q^{3}-2q^{4}+4q^{7}+q^{9}+3q^{11}+\cdots\)
9025.2.a.f $1$ $72.065$ \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(-3\) $+$ $+$ \(q-2q^{4}-3q^{7}-3q^{9}-5q^{11}+4q^{16}+\cdots\)
9025.2.a.g $1$ $72.065$ \(\Q\) None \(0\) \(2\) \(0\) \(4\) $+$ $+$ \(q+2q^{3}-2q^{4}+4q^{7}+q^{9}+3q^{11}+\cdots\)
9025.2.a.h $1$ $72.065$ \(\Q\) None \(1\) \(0\) \(0\) \(2\) $-$ $-$ \(q+q^{2}-q^{4}+2q^{7}-3q^{8}-3q^{9}-4q^{11}+\cdots\)
9025.2.a.i $1$ $72.065$ \(\Q\) None \(2\) \(0\) \(0\) \(-4\) $-$ $+$ \(q+2q^{2}+2q^{4}-4q^{7}-3q^{9}-q^{11}+\cdots\)
9025.2.a.j $1$ $72.065$ \(\Q\) None \(2\) \(0\) \(0\) \(4\) $-$ $-$ \(q+2q^{2}+2q^{4}+4q^{7}-3q^{9}-q^{11}+\cdots\)
9025.2.a.k $2$ $72.065$ \(\Q(\sqrt{5}) \) None \(-3\) \(-3\) \(0\) \(4\) $+$ $-$ \(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
9025.2.a.l $2$ $72.065$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(-4\) $-$ $-$ \(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
9025.2.a.m $2$ $72.065$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(4\) $+$ $-$ \(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
9025.2.a.n $2$ $72.065$ \(\Q(\sqrt{5}) \) None \(-1\) \(-3\) \(0\) \(-6\) $+$ $-$ \(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
9025.2.a.o $2$ $72.065$ \(\Q(\sqrt{5}) \) None \(0\) \(-4\) \(0\) \(2\) $+$ $-$ \(q+(1-2\beta )q^{2}-2q^{3}+3q^{4}+(-2+4\beta )q^{6}+\cdots\)
9025.2.a.p $2$ $72.065$ \(\Q(\sqrt{19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ \(q-2q^{4}-\beta q^{7}-3q^{9}+5q^{11}+4q^{16}+\cdots\)
9025.2.a.q $2$ $72.065$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(4\) $+$ $+$ \(q-\beta q^{2}+3q^{4}+2q^{7}-\beta q^{8}-3q^{9}+\cdots\)
9025.2.a.r $2$ $72.065$ \(\Q(\sqrt{5}) \) None \(0\) \(4\) \(0\) \(2\) $+$ $-$ \(q+(1-2\beta )q^{2}+2q^{3}+3q^{4}+(2-4\beta )q^{6}+\cdots\)
9025.2.a.s $2$ $72.065$ \(\Q(\sqrt{5}) \) None \(1\) \(3\) \(0\) \(-6\) $+$ $-$ \(q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.t $2$ $72.065$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(-4\) $-$ $-$ \(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.u $2$ $72.065$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(0\) \(4\) $+$ $-$ \(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.v $2$ $72.065$ \(\Q(\sqrt{5}) \) None \(3\) \(3\) \(0\) \(4\) $+$ $-$ \(q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+(2+\cdots)q^{6}+\cdots\)
9025.2.a.w $3$ $72.065$ \(\Q(\zeta_{14})^+\) None \(-4\) \(-2\) \(0\) \(0\) $-$ $-$ \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
9025.2.a.x $3$ $72.065$ \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(0\) \(0\) $+$ $-$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
9025.2.a.y $3$ $72.065$ 3.3.169.1 None \(-2\) \(-2\) \(0\) \(4\) $+$ $-$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
9025.2.a.z $3$ $72.065$ 3.3.361.1 None \(-1\) \(-1\) \(0\) \(-2\) $+$ $+$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
9025.2.a.ba $3$ $72.065$ 3.3.361.1 None \(1\) \(1\) \(0\) \(-2\) $+$ $-$ \(q+(1-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.bb $3$ $72.065$ 3.3.148.1 None \(1\) \(2\) \(0\) \(0\) $+$ $-$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
9025.2.a.bc $3$ $72.065$ 3.3.169.1 None \(2\) \(2\) \(0\) \(-4\) $-$ $-$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.bd $3$ $72.065$ \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(0\) \(0\) $+$ $+$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.be $3$ $72.065$ \(\Q(\zeta_{14})^+\) None \(4\) \(2\) \(0\) \(0\) $+$ $-$ \(q+(1+\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.bf $4$ $72.065$ 4.4.11344.1 None \(-2\) \(2\) \(0\) \(-4\) $+$ $-$ \(q+\beta _{2}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
9025.2.a.bg $4$ $72.065$ 4.4.7537.1 None \(-1\) \(-3\) \(0\) \(4\) $+$ $+$ \(q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)
9025.2.a.bh $4$ $72.065$ 4.4.2225.1 None \(-1\) \(-1\) \(0\) \(11\) $+$ $-$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{3})q^{4}+\cdots\)
9025.2.a.bi $4$ $72.065$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ \(q+(-\beta _{1}+\beta _{3})q^{3}-2q^{4}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
9025.2.a.bj $4$ $72.065$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(0\) \(8\) $+$ $+$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-3+\cdots)q^{6}+\cdots\)
9025.2.a.bk $4$ $72.065$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(0\) \(-8\) $+$ $+$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
9025.2.a.bl $4$ $72.065$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(0\) \(8\) $+$ $+$ \(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(3+\beta _{2}+\cdots)q^{6}+\cdots\)
9025.2.a.bm $4$ $72.065$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(0\) \(8\) $-$ $+$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
9025.2.a.bn $4$ $72.065$ 4.4.7168.1 None \(0\) \(0\) \(0\) \(-8\) $+$ $+$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
9025.2.a.bo $4$ $72.065$ 4.4.2225.1 None \(1\) \(1\) \(0\) \(11\) $+$ $-$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.bp $4$ $72.065$ 4.4.7537.1 None \(1\) \(3\) \(0\) \(4\) $+$ $-$ \(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)
9025.2.a.bq $6$ $72.065$ 6.6.5822000.1 None \(-2\) \(-4\) \(0\) \(-7\) $+$ $-$ \(q+(-1+\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
9025.2.a.br $6$ $72.065$ 6.6.41289040.1 None \(-2\) \(-3\) \(0\) \(-2\) $+$ $+$ \(q-\beta _{4}q^{2}+(-1+\beta _{1}+\beta _{3})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
9025.2.a.bs $6$ $72.065$ 6.6.41289040.1 None \(-2\) \(-3\) \(0\) \(2\) $-$ $-$ \(q-\beta _{4}q^{2}-\beta _{1}q^{3}+(-\beta _{3}+\beta _{4})q^{4}+\cdots\)
9025.2.a.bt $6$ $72.065$ 6.6.4227136.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ \(q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{1}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
9025.2.a.bu $6$ $72.065$ 6.6.4227136.1 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ \(q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{1}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
9025.2.a.bv $6$ $72.065$ 6.6.71593280.1 None \(0\) \(0\) \(0\) \(-4\) $+$ $+$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
9025.2.a.bw $6$ $72.065$ 6.6.71593280.1 None \(0\) \(0\) \(0\) \(4\) $-$ $+$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
9025.2.a.bx $6$ $72.065$ 6.6.66064384.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ \(q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
9025.2.a.by $6$ $72.065$ 6.6.41289040.1 None \(2\) \(3\) \(0\) \(-2\) $+$ $-$ \(q+\beta _{4}q^{2}+(1-\beta _{1}-\beta _{3})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
9025.2.a.bz $6$ $72.065$ 6.6.41289040.1 None \(2\) \(3\) \(0\) \(2\) $-$ $+$ \(q+\beta _{4}q^{2}+(1-\beta _{1}-\beta _{3})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
9025.2.a.ca $6$ $72.065$ 6.6.5822000.1 None \(2\) \(4\) \(0\) \(-7\) $+$ $-$ \(q+(1-\beta _{1}+\beta _{3})q^{2}+(1+\beta _{3}-\beta _{4})q^{3}+\cdots\)
9025.2.a.cb $8$ $72.065$ 8.8.\(\cdots\).1 \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
9025.2.a.cc $9$ $72.065$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-6\) \(-9\) \(0\) \(0\) $+$ $+$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{7})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
9025.2.a.cd $9$ $72.065$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(0\) \(0\) $+$ $-$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
9025.2.a.ce $9$ $72.065$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(0\) \(0\) $+$ $+$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
9025.2.a.cf $9$ $72.065$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(6\) \(9\) \(0\) \(0\) $+$ $-$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{7})q^{3}+(\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
9025.2.a.cg $10$ $72.065$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(0\) \(0\) \(-4\) $-$ $-$ \(q-\beta _{1}q^{2}+(1+\beta _{4}+\beta _{7}-\beta _{8})q^{3}+(1+\cdots)q^{4}+\cdots\)
9025.2.a.ch $10$ $72.065$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(0\) \(0\) \(4\) $+$ $-$ \(q-\beta _{1}q^{2}+(1+\beta _{4}+\beta _{7}-\beta _{8})q^{3}+(1+\cdots)q^{4}+\cdots\)
9025.2.a.ci $10$ $72.065$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(0\) \(0\) \(-4\) $-$ $-$ \(q+\beta _{1}q^{2}+(-1-\beta _{4}-\beta _{7}+\beta _{8})q^{3}+\cdots\)
9025.2.a.cj $10$ $72.065$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(0\) \(0\) \(4\) $+$ $-$ \(q+\beta _{1}q^{2}+(-1-\beta _{4}-\beta _{7}+\beta _{8})q^{3}+\cdots\)
9025.2.a.ck $16$ $72.065$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.cl $16$ $72.065$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.cm $16$ $72.065$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-22\) $+$ $+$ \(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(2-\beta _{5}+\beta _{6})q^{4}+\cdots\)
9025.2.a.cn $20$ $72.065$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(-8\) $+$ $+$ \(q+\beta _{1}q^{2}+\beta _{16}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.co $20$ $72.065$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(8\) $-$ $+$ \(q+\beta _{1}q^{2}+\beta _{16}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
9025.2.a.cp $21$ $72.065$ None \(-6\) \(-9\) \(0\) \(0\) $-$ $-$
9025.2.a.cq $21$ $72.065$ None \(-6\) \(-9\) \(0\) \(0\) $+$ $+$
9025.2.a.cr $21$ $72.065$ None \(6\) \(9\) \(0\) \(0\) $+$ $-$
9025.2.a.cs $21$ $72.065$ None \(6\) \(9\) \(0\) \(0\) $-$ $+$
9025.2.a.ct $24$ $72.065$ None \(0\) \(0\) \(0\) \(0\) $-$ $-$
9025.2.a.cu $24$ $72.065$ None \(0\) \(0\) \(0\) \(0\) $-$ $+$
9025.2.a.cv $40$ $72.065$ None \(0\) \(0\) \(0\) \(0\) $-$ $+$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1805))\)\(^{\oplus 2}\)