Space of modular forms of level 1805, weight 4, and trivial character

• Label: 1805.4.a
• Level: $1805$
• Weight: $4$
• Character orbit: 1805.a
• Rep. character: $\chi_{1805}(1,\cdot)$
• Character field: $\Q$
• Dimension: $341$
• Newform subspaces: $28$
• Sturm bound: $760$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 28 \)
Sturm bound:			\(760\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1805))\).

	Total	New	Old
Modular forms	590	341	249
Cusp forms	550	341	209
Eisenstein series	40	0	40

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

\(5\)	\(19\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(155\)	\(90\)	\(65\)		\(145\)	\(90\)	\(55\)		\(10\)	\(0\)	\(10\)
\(+\)	\(-\)	\(-\)		\(140\)	\(81\)	\(59\)		\(130\)	\(81\)	\(49\)		\(10\)	\(0\)	\(10\)
\(-\)	\(+\)	\(-\)		\(145\)	\(80\)	\(65\)		\(135\)	\(80\)	\(55\)		\(10\)	\(0\)	\(10\)
\(-\)	\(-\)	\(+\)		\(150\)	\(90\)	\(60\)		\(140\)	\(90\)	\(50\)		\(10\)	\(0\)	\(10\)
Plus space		\(+\)		\(305\)	\(180\)	\(125\)		\(285\)	\(180\)	\(105\)		\(20\)	\(0\)	\(20\)
Minus space		\(-\)		\(285\)	\(161\)	\(124\)		\(265\)	\(161\)	\(104\)		\(20\)	\(0\)	\(20\)

Trace form

341 * q - 2 * q^3 + 1380 * q^4 - 5 * q^5 - 60 * q^6 - 34 * q^7 + 48 * q^8 + 3097 * q^9 - 20 * q^10 - 40 * q^11 - 80 * q^12 + 22 * q^13 + 48 * q^14 + 50 * q^15 + 5340 * q^16 - 130 * q^17 + 16 * q^18 - 40 * q^20 - 252 * q^21 - 80 * q^22 + 66 * q^23 - 436 * q^24 + 8525 * q^25 + 852 * q^26 - 188 * q^27 + 76 * q^28 - 170 * q^29 + 120 * q^30 - 236 * q^31 + 1464 * q^32 + 432 * q^33 + 696 * q^34 - 290 * q^35 + 14240 * q^36 - 378 * q^37 + 612 * q^39 + 1062 * q^41 + 3156 * q^42 - 690 * q^43 + 240 * q^44 + 275 * q^45 + 200 * q^46 - 1378 * q^47 + 1068 * q^48 + 16093 * q^49 - 268 * q^51 - 132 * q^52 + 2430 * q^53 - 852 * q^54 - 160 * q^55 + 104 * q^56 + 1364 * q^58 + 428 * q^59 - 260 * q^60 + 810 * q^61 + 164 * q^62 - 1698 * q^63 + 22880 * q^64 + 290 * q^65 - 2496 * q^66 - 1670 * q^67 - 1256 * q^68 - 1076 * q^69 + 1480 * q^70 + 668 * q^71 + 908 * q^72 - 90 * q^73 + 1108 * q^74 - 50 * q^75 - 960 * q^77 + 2488 * q^78 - 56 * q^79 - 1120 * q^80 + 26569 * q^81 - 3788 * q^82 - 202 * q^83 - 1408 * q^84 - 370 * q^85 - 1680 * q^86 - 1588 * q^87 - 3196 * q^88 - 3150 * q^89 + 460 * q^90 - 1724 * q^91 - 4328 * q^92 - 4400 * q^93 + 1120 * q^94 + 2396 * q^96 - 2898 * q^97 - 848 * q^98 + 1400 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1805))\) 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	19
1805.4.a.a	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	\(\Q\)	None	✓				95.4.a.d	$1$	$0$	\(-5\)	\(-4\)	\(5\)	\(-32\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{2}-4q^{3}+17q^{4}+5q^{5}+20q^{6}+\cdots\)
1805.4.a.b	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	\(\Q\)	None	✓	✓			1805.4.a.b	$1$	$1$	\(-5\)	\(5\)	\(5\)	\(-19\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{2}+5q^{3}+17q^{4}+5q^{5}-5^{2}q^{6}+\cdots\)
1805.4.a.c	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	\(\Q\)	None	✓				95.4.a.c	$1$	$2$	\(-3\)	\(-7\)	\(5\)	\(11\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}-7q^{3}+q^{4}+5q^{5}+21q^{6}+\cdots\)
1805.4.a.d	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	\(\Q\)	None	✓				95.4.a.b	$1$	$1$	\(-3\)	\(5\)	\(-5\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+5q^{3}+q^{4}-5q^{5}-15q^{6}+\cdots\)
1805.4.a.e	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	\(\Q\)	None	✓				95.4.e.a	$1$	$1$	\(-1\)	\(-5\)	\(5\)	\(22\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-5q^{3}-7q^{4}+5q^{5}+5q^{6}+\cdots\)
1805.4.a.f	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	\(\Q\)	None	✓				95.4.a.a	$1$	$1$	\(0\)	\(-4\)	\(-5\)	\(-22\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-8q^{4}-5q^{5}-22q^{7}-11q^{9}+\cdots\)
1805.4.a.g	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	\(\Q\)	None	✓				95.4.e.a	$1$	$0$	\(1\)	\(5\)	\(5\)	\(22\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+5q^{3}-7q^{4}+5q^{5}+5q^{6}+\cdots\)
1805.4.a.h	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	\(\Q\)	None	✓				5.4.a.a	$1$	$1$	\(4\)	\(-2\)	\(-5\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}-2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots\)
1805.4.a.i	$1805$	$4$	1805.a	1.a	$1$	$1$	$1$	$106.498$	\(\Q\)	None	✓	✓			1805.4.a.b	$1$	$1$	\(5\)	\(-5\)	\(5\)	\(-19\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{2}-5q^{3}+17q^{4}+5q^{5}-5^{2}q^{6}+\cdots\)
1805.4.a.j	$1805$	$4$	1805.a	1.a	$1$	$3$	$3$	$106.498$	3.3.1304.1	None	✓				95.4.a.e	$1$	$0$	\(3\)	\(11\)	\(15\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(4+\beta _{1}+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
1805.4.a.k	$1805$	$4$	1805.a	1.a	$1$	$5$	$5$	$106.498$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				95.4.a.f	$1$	$0$	\(3\)	\(4\)	\(25\)	\(72\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
1805.4.a.l	$1805$	$4$	1805.a	1.a	$1$	$6$	$6$	$106.498$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			1805.4.a.l	$2$	$1$	\(0\)	\(0\)	\(30\)	\(-8\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{3}+\cdots)q^{4}+\cdots\)
1805.4.a.m	$1805$	$4$	1805.a	1.a	$1$	$6$	$6$	$106.498$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				95.4.a.g	$1$	$1$	\(1\)	\(-5\)	\(-30\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{5})q^{3}+(4+\beta _{2}+\cdots)q^{4}+\cdots\)
1805.4.a.n	$1805$	$4$	1805.a	1.a	$1$	$9$	$9$	$106.498$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				95.4.e.b	$1$	$1$	\(-6\)	\(-2\)	\(45\)	\(-45\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{5}q^{3}+(6-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1805.4.a.o	$1805$	$4$	1805.a	1.a	$1$	$9$	$9$	$106.498$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				95.4.e.b	$1$	$0$	\(6\)	\(2\)	\(45\)	\(-45\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{5}q^{3}+(6-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1805.4.a.p	$1805$	$4$	1805.a	1.a	$1$	$10$	$10$	$106.498$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				95.4.e.c	$1$	$1$	\(-3\)	\(-5\)	\(-50\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots\)
1805.4.a.q	$1805$	$4$	1805.a	1.a	$1$	$10$	$10$	$106.498$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			1805.4.a.q	$2$	$0$	\(0\)	\(0\)	\(-50\)	\(18\)		$+$	$+$	$+$	$2^{14}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(6+\beta _{2})q^{4}-5q^{5}+\cdots\)
1805.4.a.r	$1805$	$4$	1805.a	1.a	$1$	$10$	$10$	$106.498$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				95.4.e.c	$1$	$0$	\(3\)	\(5\)	\(-50\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(4+\beta _{2})q^{4}-5q^{5}+\cdots\)
1805.4.a.s	$1805$	$4$	1805.a	1.a	$1$	$16$	$16$	$106.498$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓			1805.4.a.s	$1$	$1$	\(-1\)	\(-2\)	\(-80\)	\(-26\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(4+\beta _{2}+\beta _{3})q^{4}+\cdots\)
1805.4.a.t	$1805$	$4$	1805.a	1.a	$1$	$16$	$16$	$106.498$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓			1805.4.a.s	$1$	$1$	\(1\)	\(2\)	\(-80\)	\(-26\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(4+\beta _{2}+\beta _{3})q^{4}+\cdots\)
1805.4.a.u	$1805$	$4$	1805.a	1.a	$1$	$20$	$20$	$106.498$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓			1805.4.a.u	$1$	$0$	\(-1\)	\(2\)	\(100\)	\(82\)		$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{9}q^{3}+(5+\beta _{2})q^{4}+5q^{5}+\cdots\)
1805.4.a.v	$1805$	$4$	1805.a	1.a	$1$	$20$	$20$	$106.498$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓			1805.4.a.u	$1$	$0$	\(1\)	\(-2\)	\(100\)	\(82\)		$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(5+\beta _{2})q^{4}+5q^{5}+\cdots\)
1805.4.a.w	$1805$	$4$	1805.a	1.a	$1$	$30$	$30$	$106.498$		None	✓				95.4.k.a	$1$	$1$	\(-12\)	\(-36\)	\(150\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
1805.4.a.x	$1805$	$4$	1805.a	1.a	$1$	$30$	$30$	$106.498$		None	✓				95.4.k.b	$1$	$0$	\(0\)	\(0\)	\(-150\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
1805.4.a.y	$1805$	$4$	1805.a	1.a	$1$	$30$	$30$	$106.498$		None	✓		✓		95.4.k.b	$1$	$1$	\(0\)	\(0\)	\(-150\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
1805.4.a.z	$1805$	$4$	1805.a	1.a	$1$	$30$	$30$	$106.498$		None	✓		✓		95.4.k.a	$1$	$0$	\(12\)	\(36\)	\(150\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
1805.4.a.ba	$1805$	$4$	1805.a	1.a	$1$	$32$	$32$	$106.498$		None	✓	✓	✓		1805.4.a.ba	$2$	$1$	\(0\)	\(0\)	\(160\)	\(-164\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
1805.4.a.bb	$1805$	$4$	1805.a	1.a	$1$	$40$	$40$	$106.498$		None	✓	✓	✓		1805.4.a.bb	$2$	$0$	\(0\)	\(0\)	\(-200\)	\(52\)		$+$	$+$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1805))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1805)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 2}\)