Space of modular forms of level 4205, weight 2, and trivial character

• Label: 4205.2.a
• Level: $4205$
• Weight: $2$
• Character orbit: 4205.a
• Rep. character: $\chi_{4205}(1,\cdot)$
• Character field: $\Q$
• Dimension: $271$
• Newform subspaces: $26$
• Sturm bound: $870$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 4205 = 5 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4205.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(870\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4205))\).

	Total	New	Old
Modular forms	464	271	193
Cusp forms	405	271	134
Eisenstein series	59	0	59

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

\(5\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(61\)
\(+\)	\(-\)	\(-\)	\(75\)
\(-\)	\(+\)	\(-\)	\(74\)
\(-\)	\(-\)	\(+\)	\(61\)
Plus space		\(+\)	\(122\)
Minus space		\(-\)	\(149\)

Trace form

271 * q - q^2 + 4 * q^3 + 273 * q^4 - q^5 - 4 * q^6 + 4 * q^7 - 9 * q^8 + 275 * q^9 + 3 * q^10 + 16 * q^12 + 10 * q^13 + 8 * q^14 + 273 * q^16 + 6 * q^17 + 7 * q^18 + 16 * q^19 + q^20 - 24 * q^22 - 20 * q^23 + 271 * q^25 + 2 * q^26 - 8 * q^27 - 16 * q^28 + 4 * q^30 + 4 * q^31 - 9 * q^32 + 8 * q^33 + 6 * q^34 - 4 * q^35 + 301 * q^36 - 6 * q^37 + 12 * q^38 - 32 * q^39 + 15 * q^40 + 22 * q^41 - 20 * q^42 + 12 * q^43 - 5 * q^45 - 40 * q^46 - 8 * q^47 + 12 * q^48 + 279 * q^49 - q^50 - 6 * q^52 - 22 * q^53 - 24 * q^54 + 4 * q^55 + 24 * q^56 - 8 * q^59 + 12 * q^60 + 2 * q^61 - 44 * q^62 - 20 * q^63 + 253 * q^64 + 2 * q^65 + 16 * q^66 - 20 * q^67 + 38 * q^68 - 16 * q^69 - 12 * q^70 - 40 * q^71 + 31 * q^72 + 26 * q^73 + 42 * q^74 + 4 * q^75 - 16 * q^76 - 4 * q^77 + 12 * q^78 - 4 * q^79 + q^80 + 287 * q^81 - 26 * q^82 - 20 * q^83 + 16 * q^84 + 2 * q^85 - 12 * q^86 - 76 * q^88 - 26 * q^89 - 13 * q^90 + 4 * q^92 - 8 * q^93 - 24 * q^94 + 12 * q^95 - 28 * q^96 + 34 * q^97 - 69 * q^98 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4205))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	29
4205.2.a.a	$4205$	$2$	4205.a	1.a	$1$	$1$	$1$	$33.577$	\(\Q\)	None	✓				145.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-2q^{7}-3q^{8}-3q^{9}+\cdots\)
4205.2.a.b	$4205$	$2$	4205.a	1.a	$1$	$2$	$2$	$33.577$	\(\Q(\sqrt{5}) \)	None	✓	✓			4205.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{5}+(-1-2\beta )q^{7}+\cdots\)
4205.2.a.c	$4205$	$2$	4205.a	1.a	$1$	$2$	$2$	$33.577$	\(\Q(\sqrt{5}) \)	None	✓	✓			4205.2.a.b	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{5}+(-1-2\beta )q^{7}+\cdots\)
4205.2.a.d	$4205$	$2$	4205.a	1.a	$1$	$2$	$2$	$33.577$	\(\Q(\sqrt{2}) \)	None	✓				145.2.a.b	$1$	$0$	\(2\)	\(4\)	\(2\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+2q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
4205.2.a.e	$4205$	$2$	4205.a	1.a	$1$	$3$	$3$	$33.577$	3.3.148.1	None	✓				145.2.a.d	$1$	$1$	\(-3\)	\(2\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
4205.2.a.f	$4205$	$2$	4205.a	1.a	$1$	$3$	$3$	$33.577$	3.3.148.1	None	✓				145.2.a.c	$1$	$0$	\(-1\)	\(-2\)	\(3\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
4205.2.a.g	$4205$	$2$	4205.a	1.a	$1$	$4$	$4$	$33.577$	\(\Q(\zeta_{24})^+\)	None	✓				145.2.c.a	$2$	$1$	\(0\)	\(0\)	\(4\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+q^{5}+\cdots\)
4205.2.a.h	$4205$	$2$	4205.a	1.a	$1$	$5$	$5$	$33.577$	5.5.1586009.1	None	✓	✓			4205.2.a.h	$1$	$1$	\(-1\)	\(-2\)	\(5\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{3}-\beta _{4})q^{4}+\cdots\)
4205.2.a.i	$4205$	$2$	4205.a	1.a	$1$	$5$	$5$	$33.577$	5.5.942577.1	None	✓	✓			4205.2.a.i	$1$	$0$	\(-1\)	\(2\)	\(-5\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
4205.2.a.j	$4205$	$2$	4205.a	1.a	$1$	$5$	$5$	$33.577$	5.5.942577.1	None	✓	✓			4205.2.a.i	$1$	$1$	\(1\)	\(-2\)	\(-5\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
4205.2.a.k	$4205$	$2$	4205.a	1.a	$1$	$5$	$5$	$33.577$	5.5.1586009.1	None	✓	✓			4205.2.a.h	$1$	$0$	\(1\)	\(2\)	\(5\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(2+\beta _{3}-\beta _{4})q^{4}+\cdots\)
4205.2.a.l	$4205$	$2$	4205.a	1.a	$1$	$6$	$6$	$33.577$	6.6.5516125.1	None	✓	✓			4205.2.a.l	$1$	$0$	\(-1\)	\(-1\)	\(-6\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{2}-\beta _{3}+\beta _{4})q^{3}+(1+\cdots)q^{4}+\cdots\)
4205.2.a.m	$4205$	$2$	4205.a	1.a	$1$	$6$	$6$	$33.577$	6.6.66064384.1	None	✓				145.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4205.2.a.n	$4205$	$2$	4205.a	1.a	$1$	$6$	$6$	$33.577$	6.6.5516125.1	None	✓	✓			4205.2.a.l	$1$	$1$	\(1\)	\(1\)	\(-6\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
4205.2.a.o	$4205$	$2$	4205.a	1.a	$1$	$8$	$8$	$33.577$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			4205.2.a.o	$1$	$1$	\(-3\)	\(-7\)	\(8\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4205.2.a.p	$4205$	$2$	4205.a	1.a	$1$	$8$	$8$	$33.577$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			4205.2.a.o	$1$	$0$	\(3\)	\(7\)	\(8\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4205.2.a.q	$4205$	$2$	4205.a	1.a	$1$	$12$	$12$	$33.577$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				145.2.k.a	$1$	$1$	\(-1\)	\(1\)	\(-12\)	\(-5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}-q^{5}+(-2+\cdots)q^{6}+\cdots\)
4205.2.a.r	$4205$	$2$	4205.a	1.a	$1$	$12$	$12$	$33.577$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				145.2.k.a	$1$	$1$	\(1\)	\(-1\)	\(-12\)	\(-5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{11}q^{3}+\beta _{2}q^{4}-q^{5}+(-2+\cdots)q^{6}+\cdots\)
4205.2.a.s	$4205$	$2$	4205.a	1.a	$1$	$18$	$18$	$33.577$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓				145.2.k.b	$1$	$0$	\(-1\)	\(-1\)	\(18\)	\(17\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4205.2.a.t	$4205$	$2$	4205.a	1.a	$1$	$18$	$18$	$33.577$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓				145.2.k.b	$1$	$0$	\(1\)	\(1\)	\(18\)	\(17\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4205.2.a.u	$4205$	$2$	4205.a	1.a	$1$	$20$	$20$	$33.577$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓			4205.2.a.u	$1$	$1$	\(-9\)	\(-13\)	\(20\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4205.2.a.v	$4205$	$2$	4205.a	1.a	$1$	$20$	$20$	$33.577$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓		4205.2.a.v	$1$	$1$	\(-1\)	\(-3\)	\(-20\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{17}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
4205.2.a.w	$4205$	$2$	4205.a	1.a	$1$	$20$	$20$	$33.577$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓			4205.2.a.v	$1$	$0$	\(1\)	\(3\)	\(-20\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{17}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
4205.2.a.x	$4205$	$2$	4205.a	1.a	$1$	$20$	$20$	$33.577$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓		4205.2.a.u	$1$	$0$	\(9\)	\(13\)	\(20\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4205.2.a.y	$4205$	$2$	4205.a	1.a	$1$	$24$	$24$	$33.577$		None	✓		✓		145.2.m.a	$2$	$1$	\(0\)	\(0\)	\(24\)	\(-38\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4205.2.a.z	$4205$	$2$	4205.a	1.a	$1$	$36$	$36$	$33.577$		None	✓		✓		145.2.m.b	$2$	$0$	\(0\)	\(0\)	\(-36\)	\(14\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4205))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4205)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(841))\)\(^{\oplus 2}\)