Properties

Label 2205.4.a
Level $2205$
Weight $4$
Character orbit 2205.a
Rep. character $\chi_{2205}(1,\cdot)$
Character field $\Q$
Dimension $205$
Newform subspaces $61$
Sturm bound $1344$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 61 \)
Sturm bound: \(1344\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2205))\).

Total New Old
Modular forms 1040 205 835
Cusp forms 976 205 771
Eisenstein series 64 0 64

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

\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(20\)
\(+\)\(+\)\(-\)\(-\)\(21\)
\(+\)\(-\)\(+\)\(-\)\(20\)
\(+\)\(-\)\(-\)\(+\)\(21\)
\(-\)\(+\)\(+\)\(-\)\(29\)
\(-\)\(+\)\(-\)\(+\)\(33\)
\(-\)\(-\)\(+\)\(+\)\(31\)
\(-\)\(-\)\(-\)\(-\)\(30\)
Plus space\(+\)\(105\)
Minus space\(-\)\(100\)

Trace form

\( 205 q + 4 q^{2} + 816 q^{4} - 5 q^{5} + O(q^{10}) \) \( 205 q + 4 q^{2} + 816 q^{4} - 5 q^{5} - 20 q^{10} - 80 q^{11} - 34 q^{13} + 3240 q^{16} - 194 q^{17} - 64 q^{19} - 80 q^{20} - 512 q^{22} - 130 q^{23} + 5125 q^{25} - 72 q^{26} + 422 q^{29} + 412 q^{31} + 104 q^{32} - 552 q^{34} + 1050 q^{37} - 1540 q^{38} - 180 q^{40} + 830 q^{41} - 246 q^{43} - 2464 q^{44} - 236 q^{46} - 554 q^{47} + 100 q^{50} + 416 q^{52} + 1286 q^{53} - 80 q^{55} + 724 q^{58} - 1652 q^{59} + 2158 q^{61} - 936 q^{62} + 12568 q^{64} + 290 q^{65} + 926 q^{67} - 244 q^{68} + 28 q^{71} + 618 q^{73} - 648 q^{74} - 1548 q^{76} - 1192 q^{79} - 2320 q^{80} + 1492 q^{82} + 1166 q^{83} - 210 q^{85} - 7800 q^{86} - 11072 q^{88} - 3030 q^{89} - 2324 q^{92} + 2916 q^{94} + 500 q^{95} + 2170 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2205))\) 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 5 7
2205.4.a.a 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-5\) \(0\) \(-5\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-5q^{2}+17q^{4}-5q^{5}-45q^{8}+5^{2}q^{10}+\cdots\)
2205.4.a.b 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-5\) \(0\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-5q^{2}+17q^{4}+5q^{5}-45q^{8}-5^{2}q^{10}+\cdots\)
2205.4.a.c 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-3\) \(0\) \(-5\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}-5q^{5}+21q^{8}+15q^{10}+\cdots\)
2205.4.a.d 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-3\) \(0\) \(-5\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}-5q^{5}+21q^{8}+15q^{10}+\cdots\)
2205.4.a.e 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-3\) \(0\) \(-5\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}-5q^{5}+21q^{8}+15q^{10}+\cdots\)
2205.4.a.f 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-3\) \(0\) \(5\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}+5q^{5}+21q^{8}-15q^{10}+\cdots\)
2205.4.a.g 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-3\) \(0\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}+5q^{5}+21q^{8}-15q^{10}+\cdots\)
2205.4.a.h 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-3\) \(0\) \(5\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}+5q^{5}+21q^{8}-15q^{10}+\cdots\)
2205.4.a.i 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-1\) \(0\) \(-5\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}-5q^{5}+15q^{8}+5q^{10}+\cdots\)
2205.4.a.j 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-1\) \(0\) \(-5\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}-5q^{5}+15q^{8}+5q^{10}+\cdots\)
2205.4.a.k 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-1\) \(0\) \(-5\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}-5q^{5}+15q^{8}+5q^{10}+\cdots\)
2205.4.a.l 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-1\) \(0\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}+5q^{5}+15q^{8}-5q^{10}+\cdots\)
2205.4.a.m 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-1\) \(0\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}+5q^{5}+15q^{8}-5q^{10}+\cdots\)
2205.4.a.n 2205.a 1.a $1$ $130.099$ \(\Q\) None \(-1\) \(0\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}+5q^{5}+15q^{8}-5q^{10}+\cdots\)
2205.4.a.o 2205.a 1.a $1$ $130.099$ \(\Q\) None \(0\) \(0\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{4}+5q^{5}-42q^{11}-20q^{13}+\cdots\)
2205.4.a.p 2205.a 1.a $1$ $130.099$ \(\Q\) None \(3\) \(0\) \(-5\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{2}+q^{4}-5q^{5}-21q^{8}-15q^{10}+\cdots\)
2205.4.a.q 2205.a 1.a $1$ $130.099$ \(\Q\) None \(4\) \(0\) \(-5\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+8q^{4}-5q^{5}-20q^{10}-2^{5}q^{11}+\cdots\)
2205.4.a.r 2205.a 1.a $1$ $130.099$ \(\Q\) None \(4\) \(0\) \(-5\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+8q^{4}-5q^{5}-20q^{10}+10q^{11}+\cdots\)
2205.4.a.s 2205.a 1.a $1$ $130.099$ \(\Q\) None \(4\) \(0\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+8q^{4}+5q^{5}+20q^{10}+10q^{11}+\cdots\)
2205.4.a.t 2205.a 1.a $1$ $130.099$ \(\Q\) None \(5\) \(0\) \(5\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{2}+17q^{4}+5q^{5}+45q^{8}+5^{2}q^{10}+\cdots\)
2205.4.a.u 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{2}) \) None \(-8\) \(0\) \(-10\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-4+\beta )q^{2}+(10-8\beta )q^{4}-5q^{5}+\cdots\)
2205.4.a.v 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{41}) \) None \(-3\) \(0\) \(-10\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(3+3\beta )q^{4}-5q^{5}+\cdots\)
2205.4.a.w 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{11}) \) None \(-2\) \(0\) \(-10\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(4-2\beta )q^{4}-5q^{5}+\cdots\)
2205.4.a.x 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{11}) \) None \(-2\) \(0\) \(10\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(4-2\beta )q^{4}+5q^{5}+\cdots\)
2205.4.a.y 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{17}) \) None \(-1\) \(0\) \(10\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-4+\beta )q^{4}+5q^{5}+(-4+\cdots)q^{8}+\cdots\)
2205.4.a.z 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{65}) \) None \(-1\) \(0\) \(10\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(8+\beta )q^{4}+5q^{5}+(-2^{4}-\beta )q^{8}+\cdots\)
2205.4.a.ba 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(-10\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-4+\beta )q^{4}-5q^{5}+(4-11\beta )q^{8}+\cdots\)
2205.4.a.bb 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(10\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+5q^{5}+(9+\cdots)q^{8}+\cdots\)
2205.4.a.bc 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(-10\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{2}+(-2+4\beta )q^{4}-5q^{5}+\cdots\)
2205.4.a.bd 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(10\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{2}+(-2+4\beta )q^{4}+5q^{5}+\cdots\)
2205.4.a.be 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{5}) \) None \(4\) \(0\) \(-10\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{2}+(1+4\beta )q^{4}-5q^{5}+(6+\cdots)q^{8}+\cdots\)
2205.4.a.bf 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{2}) \) None \(6\) \(0\) \(-10\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(3+\beta )q^{2}+(3+6\beta )q^{4}-5q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.4.a.bg 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{2}) \) None \(6\) \(0\) \(10\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(3+\beta )q^{2}+(3+6\beta )q^{4}+5q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.4.a.bh 2205.a 1.a $2$ $130.099$ \(\Q(\sqrt{17}) \) None \(7\) \(0\) \(-10\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(4-\beta )q^{2}+(12-7\beta )q^{4}-5q^{5}+(44+\cdots)q^{8}+\cdots\)
2205.4.a.bi 2205.a 1.a $3$ $130.099$ 3.3.4892.1 None \(-3\) \(0\) \(-15\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.bj 2205.a 1.a $3$ $130.099$ 3.3.4892.1 None \(-3\) \(0\) \(15\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.bk 2205.a 1.a $3$ $130.099$ 3.3.22952.1 None \(-2\) \(0\) \(15\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(5-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
2205.4.a.bl 2205.a 1.a $3$ $130.099$ 3.3.22952.1 None \(2\) \(0\) \(-15\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(5-2\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.bm 2205.a 1.a $3$ $130.099$ 3.3.14360.1 None \(3\) \(0\) \(15\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(4-\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.bn 2205.a 1.a $4$ $130.099$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-1\) \(0\) \(-20\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(10+\beta _{2})q^{4}-5q^{5}+(-7+\cdots)q^{8}+\cdots\)
2205.4.a.bo 2205.a 1.a $4$ $130.099$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-1\) \(0\) \(20\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(10+\beta _{2})q^{4}+5q^{5}+(-7+\cdots)q^{8}+\cdots\)
2205.4.a.bp 2205.a 1.a $4$ $130.099$ 4.4.51264.1 None \(6\) \(0\) \(-20\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1}-\beta _{2})q^{2}+(6-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
2205.4.a.bq 2205.a 1.a $4$ $130.099$ 4.4.51264.1 None \(6\) \(0\) \(20\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1}-\beta _{2})q^{2}+(6-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
2205.4.a.br 2205.a 1.a $5$ $130.099$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-3\) \(0\) \(-25\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.bs 2205.a 1.a $5$ $130.099$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-3\) \(0\) \(25\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(5+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.bt 2205.a 1.a $5$ $130.099$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-1\) \(0\) \(-25\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(7+\beta _{3})q^{4}-5q^{5}+(-4+\cdots)q^{8}+\cdots\)
2205.4.a.bu 2205.a 1.a $5$ $130.099$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-1\) \(0\) \(25\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(7+\beta _{3})q^{4}+5q^{5}+(-4+\cdots)q^{8}+\cdots\)
2205.4.a.bv 2205.a 1.a $5$ $130.099$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(0\) \(-25\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(4+\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.bw 2205.a 1.a $5$ $130.099$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(0\) \(25\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(4+\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.bx 2205.a 1.a $6$ $130.099$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(-30\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-5q^{5}+(4\beta _{1}+\cdots)q^{8}+\cdots\)
2205.4.a.by 2205.a 1.a $6$ $130.099$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(30\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+5q^{5}+(4\beta _{1}+\cdots)q^{8}+\cdots\)
2205.4.a.bz 2205.a 1.a $6$ $130.099$ 6.6.1163891200.1 None \(2\) \(0\) \(-30\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+3\beta _{1}+2\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2205.4.a.ca 2205.a 1.a $6$ $130.099$ 6.6.1163891200.1 None \(2\) \(0\) \(30\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+3\beta _{1}+2\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2205.4.a.cb 2205.a 1.a $8$ $130.099$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(0\) \(-40\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(6-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2205.4.a.cc 2205.a 1.a $8$ $130.099$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(0\) \(40\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(6-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2205.4.a.cd 2205.a 1.a $8$ $130.099$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(0\) \(-40\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(6+\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.ce 2205.a 1.a $8$ $130.099$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(0\) \(40\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(6+\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.cf 2205.a 1.a $8$ $130.099$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(0\) \(-40\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(6-\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
2205.4.a.cg 2205.a 1.a $8$ $130.099$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(0\) \(40\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(6-\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
2205.4.a.ch 2205.a 1.a $12$ $130.099$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-60\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-5q^{5}+(-\beta _{7}+\cdots)q^{8}+\cdots\)
2205.4.a.ci 2205.a 1.a $12$ $130.099$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(60\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+5q^{5}+(-\beta _{7}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2205))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2205)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 2}\)