Space of modular forms of level 1805, weight 2, and trivial character

• Label: 1805.2.a
• Level: $1805$
• Weight: $2$
• Character orbit: 1805.a
• Rep. character: $\chi_{1805}(1,\cdot)$
• Character field: $\Q$
• Dimension: $113$
• Newform subspaces: $23$
• Sturm bound: $380$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 23 \)
Sturm bound:			\(380\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1805))\).

	Total	New	Old
Modular forms	210	113	97
Cusp forms	171	113	58
Eisenstein series	39	0	39

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	Dim
\(+\)	\(+\)	\(+\)	\(23\)
\(+\)	\(-\)	\(-\)	\(33\)
\(-\)	\(+\)	\(-\)	\(33\)
\(-\)	\(-\)	\(+\)	\(24\)
Plus space		\(+\)	\(47\)
Minus space		\(-\)	\(66\)

Trace form

113 * q + q^2 - 4 * q^3 + 111 * q^4 + q^5 + 4 * q^6 - 4 * q^7 + 9 * q^8 + 109 * q^9 - 3 * q^10 + 4 * q^11 + 4 * q^12 - 10 * q^13 + 12 * q^14 + 119 * q^16 - 6 * q^17 + 29 * q^18 + 7 * q^20 + 16 * q^21 + 12 * q^22 + 12 * q^23 + 20 * q^24 + 113 * q^25 - 6 * q^26 - 4 * q^27 - 4 * q^28 + 6 * q^29 - 4 * q^30 - 8 * q^31 + 9 * q^32 - 12 * q^33 - 14 * q^34 + 4 * q^35 + 83 * q^36 - 14 * q^37 - 4 * q^39 - 15 * q^40 - 14 * q^41 - 28 * q^42 - 20 * q^44 + 5 * q^45 - 12 * q^46 - 48 * q^48 + 89 * q^49 + q^50 + 32 * q^51 - 22 * q^52 - 6 * q^53 - 20 * q^54 + 12 * q^55 - 4 * q^56 - 10 * q^58 + 20 * q^59 + 16 * q^60 - 26 * q^61 - 60 * q^62 + 123 * q^64 - 6 * q^65 - 8 * q^66 + 16 * q^67 - 14 * q^68 - 16 * q^69 - 4 * q^70 + 24 * q^71 + 65 * q^72 - 38 * q^73 - 54 * q^74 - 4 * q^75 + 32 * q^77 + 16 * q^79 - q^80 + 97 * q^81 - 18 * q^82 + 24 * q^83 + 24 * q^84 + 2 * q^85 + 24 * q^86 + 44 * q^87 + 16 * q^88 - 6 * q^89 - 39 * q^90 + 16 * q^91 + 8 * q^92 + 40 * q^93 + 52 * q^94 + 4 * q^96 - 50 * q^97 - 23 * q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1805))\) 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
1805.2.a.a	$1805$	$2$	1805.a	1.a	$1$	$1$	$1$	$14.413$	\(\Q\)	None	✓				95.2.e.a	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}-q^{5}-4q^{7}+q^{9}+3q^{11}+\cdots\)
1805.2.a.b	$1805$	$2$	1805.a	1.a	$1$	$1$	$1$	$14.413$	\(\Q\)	None	✓				95.2.e.a	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{4}-q^{5}-4q^{7}+q^{9}+3q^{11}+\cdots\)
1805.2.a.c	$1805$	$2$	1805.a	1.a	$1$	$2$	$2$	$14.413$	\(\Q(\sqrt{5}) \)	None	✓	✓			1805.2.a.c	$1$	$2$	\(-3\)	\(-3\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1805.2.a.d	$1805$	$2$	1805.a	1.a	$1$	$2$	$2$	$14.413$	\(\Q(\sqrt{5}) \)	None	✓	✓			1805.2.a.d	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+3q^{4}-q^{5}-2q^{7}-\beta q^{8}+\cdots\)
1805.2.a.e	$1805$	$2$	1805.a	1.a	$1$	$2$	$2$	$14.413$	\(\Q(\sqrt{5}) \)	None	✓	✓			1805.2.a.c	$1$	$0$	\(3\)	\(3\)	\(-2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}-q^{5}+\cdots\)
1805.2.a.f	$1805$	$2$	1805.a	1.a	$1$	$3$	$3$	$14.413$	3.3.148.1	None	✓				95.2.a.a	$1$	$1$	\(-1\)	\(-2\)	\(3\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
1805.2.a.g	$1805$	$2$	1805.a	1.a	$1$	$3$	$3$	$14.413$	3.3.361.1	None	✓				95.2.e.b	$1$	$0$	\(-1\)	\(-1\)	\(-3\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
1805.2.a.h	$1805$	$2$	1805.a	1.a	$1$	$3$	$3$	$14.413$	3.3.361.1	None	✓				95.2.e.b	$1$	$1$	\(1\)	\(1\)	\(-3\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
1805.2.a.i	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.7537.1	None	✓				95.2.e.c	$1$	$1$	\(-1\)	\(-3\)	\(4\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)
1805.2.a.j	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.2225.1	None	✓	✓			1805.2.a.j	$1$	$1$	\(-1\)	\(-1\)	\(4\)	\(-11\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{3})q^{4}+\cdots\)
1805.2.a.k	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	\(\Q(\zeta_{20})^+\)	None	✓	✓			1805.2.a.k	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{3})q^{3}-2q^{4}-q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
1805.2.a.l	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	\(\Q(\zeta_{20})^+\)	None	✓	✓			1805.2.a.l	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
1805.2.a.m	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.7168.1	None	✓	✓			1805.2.a.m	$2$	$0$	\(0\)	\(0\)	\(4\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1805.2.a.n	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.2225.1	None	✓	✓			1805.2.a.j	$1$	$1$	\(1\)	\(1\)	\(4\)	\(-11\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
1805.2.a.o	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.7537.1	None	✓				95.2.e.c	$1$	$0$	\(1\)	\(3\)	\(4\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)
1805.2.a.p	$1805$	$2$	1805.a	1.a	$1$	$4$	$4$	$14.413$	4.4.11344.1	None	✓				95.2.a.b	$1$	$0$	\(2\)	\(-2\)	\(-4\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
1805.2.a.q	$1805$	$2$	1805.a	1.a	$1$	$6$	$6$	$14.413$	6.6.5822000.1	None	✓	✓			1805.2.a.q	$1$	$0$	\(-2\)	\(-4\)	\(-6\)	\(7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
1805.2.a.r	$1805$	$2$	1805.a	1.a	$1$	$6$	$6$	$14.413$	6.6.5822000.1	None	✓	✓			1805.2.a.q	$1$	$0$	\(2\)	\(4\)	\(-6\)	\(7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{3})q^{2}+(1+\beta _{3}-\beta _{4})q^{3}+\cdots\)
1805.2.a.s	$1805$	$2$	1805.a	1.a	$1$	$9$	$9$	$14.413$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		95.2.k.a	$1$	$1$	\(-6\)	\(-9\)	\(9\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{7})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
1805.2.a.t	$1805$	$2$	1805.a	1.a	$1$	$9$	$9$	$14.413$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		95.2.k.b	$1$	$1$	\(0\)	\(-3\)	\(-9\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
1805.2.a.u	$1805$	$2$	1805.a	1.a	$1$	$9$	$9$	$14.413$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		95.2.k.b	$1$	$0$	\(0\)	\(3\)	\(-9\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1805.2.a.v	$1805$	$2$	1805.a	1.a	$1$	$9$	$9$	$14.413$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				95.2.k.a	$1$	$0$	\(6\)	\(9\)	\(9\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{7})q^{3}+(\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
1805.2.a.w	$1805$	$2$	1805.a	1.a	$1$	$16$	$16$	$14.413$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓		1805.2.a.w	$2$	$0$	\(0\)	\(0\)	\(16\)	\(22\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(2-\beta _{5}+\beta _{6})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1805))\) into lower level spaces

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