Space of modular forms of level 1445, weight 2, and trivial character

• Label: 1445.2.a
• Level: $1445$
• Weight: $2$
• Character orbit: 1445.a
• Rep. character: $\chi_{1445}(1,\cdot)$
• Character field: $\Q$
• Dimension: $91$
• Newform subspaces: $19$
• Sturm bound: $306$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(306\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1445))\).

	Total	New	Old
Modular forms	170	91	79
Cusp forms	135	91	44
Eisenstein series	35	0	35

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

\(5\)	\(17\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(36\)	\(18\)	\(18\)		\(28\)	\(18\)	\(10\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)		\(49\)	\(27\)	\(22\)		\(40\)	\(27\)	\(13\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)		\(45\)	\(27\)	\(18\)		\(36\)	\(27\)	\(9\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)		\(40\)	\(19\)	\(21\)		\(31\)	\(19\)	\(12\)		\(9\)	\(0\)	\(9\)
Plus space		\(+\)		\(76\)	\(37\)	\(39\)		\(59\)	\(37\)	\(22\)		\(17\)	\(0\)	\(17\)
Minus space		\(-\)		\(94\)	\(54\)	\(40\)		\(76\)	\(54\)	\(22\)		\(18\)	\(0\)	\(18\)

Trace form

91 * q + q^2 + 93 * q^4 + q^5 + 4 * q^6 + 8 * q^7 + 9 * q^8 + 87 * q^9 - q^10 - 4 * q^12 + 6 * q^13 - 12 * q^14 - 4 * q^15 + 101 * q^16 - 7 * q^18 - 4 * q^19 - q^20 - 8 * q^22 + 4 * q^23 - 8 * q^24 + 91 * q^25 - 2 * q^26 + 12 * q^27 + 12 * q^28 + 10 * q^29 + 8 * q^30 - 11 * q^32 - 36 * q^33 - 4 * q^35 + 121 * q^36 + 10 * q^37 - 4 * q^38 - 4 * q^39 - 9 * q^40 - 14 * q^41 - 12 * q^42 + 12 * q^44 + 5 * q^45 - 24 * q^46 - 24 * q^47 + 24 * q^48 + 103 * q^49 + q^50 - 6 * q^52 - 26 * q^53 + 20 * q^54 - 12 * q^55 - 16 * q^56 - 2 * q^58 + 6 * q^61 - 8 * q^62 + 12 * q^63 + 89 * q^64 + 10 * q^65 + 4 * q^66 + 20 * q^67 - 24 * q^69 - 12 * q^70 - 4 * q^71 - 31 * q^72 + 26 * q^73 - 18 * q^74 - 32 * q^76 - 32 * q^77 - 36 * q^78 + 8 * q^79 + 15 * q^80 + 43 * q^81 + 6 * q^82 - 32 * q^83 - 36 * q^84 - 8 * q^86 - 28 * q^88 + 14 * q^89 + 23 * q^90 + 4 * q^91 + 8 * q^92 - 4 * q^93 - 4 * q^95 - 12 * q^96 - 2 * q^97 + 21 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1445))\) 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	17
1445.2.a.a	$1445$	$2$	1445.a	1.a	$1$	$1$	$1$	$11.538$	\(\Q\)	None	✓	✓			1445.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-3q^{11}+\cdots\)
1445.2.a.b	$1445$	$2$	1445.a	1.a	$1$	$1$	$1$	$11.538$	\(\Q\)	None	✓	✓			1445.2.a.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots\)
1445.2.a.c	$1445$	$2$	1445.a	1.a	$1$	$1$	$1$	$11.538$	\(\Q\)	None	✓				85.2.a.a	$1$	$0$	\(1\)	\(-2\)	\(1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}-q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
1445.2.a.d	$1445$	$2$	1445.a	1.a	$1$	$1$	$1$	$11.538$	\(\Q\)	None	✓	✓			1445.2.a.d	$1$	$0$	\(1\)	\(-1\)	\(-1\)	\(-5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-5q^{7}+\cdots\)
1445.2.a.e	$1445$	$2$	1445.a	1.a	$1$	$1$	$1$	$11.538$	\(\Q\)	None	✓	✓			1445.2.a.d	$1$	$0$	\(1\)	\(1\)	\(1\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+5q^{7}+\cdots\)
1445.2.a.f	$1445$	$2$	1445.a	1.a	$1$	$2$	$2$	$11.538$	\(\Q(\sqrt{2}) \)	None	✓				85.2.a.b	$1$	$0$	\(-2\)	\(4\)	\(2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(2+\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
1445.2.a.g	$1445$	$2$	1445.a	1.a	$1$	$2$	$2$	$11.538$	\(\Q(\sqrt{3}) \)	None	✓				85.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(3+\cdots)q^{6}+\cdots\)
1445.2.a.h	$1445$	$2$	1445.a	1.a	$1$	$2$	$2$	$11.538$	\(\Q(\sqrt{17}) \)	None	✓	✓			1445.2.a.h	$1$	$0$	\(1\)	\(-1\)	\(-2\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-\beta q^{3}+(2+\beta )q^{4}-q^{5}+(-4+\cdots)q^{6}+\cdots\)
1445.2.a.i	$1445$	$2$	1445.a	1.a	$1$	$2$	$2$	$11.538$	\(\Q(\sqrt{17}) \)	None	✓	✓			1445.2.a.h	$1$	$0$	\(1\)	\(1\)	\(2\)	\(-5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+\beta q^{3}+(2+\beta )q^{4}+q^{5}+(4+\cdots)q^{6}+\cdots\)
1445.2.a.j	$1445$	$2$	1445.a	1.a	$1$	$3$	$3$	$11.538$	3.3.148.1	None	✓				85.2.d.a	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
1445.2.a.k	$1445$	$2$	1445.a	1.a	$1$	$3$	$3$	$11.538$	3.3.148.1	None	✓				85.2.d.a	$1$	$0$	\(1\)	\(0\)	\(3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
1445.2.a.l	$1445$	$2$	1445.a	1.a	$1$	$6$	$6$	$11.538$	6.6.1397493.1	None	✓	✓			1445.2.a.l	$1$	$1$	\(-3\)	\(-3\)	\(6\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{5})q^{2}+(-\beta _{1}+\beta _{4})q^{3}+\cdots\)
1445.2.a.m	$1445$	$2$	1445.a	1.a	$1$	$6$	$6$	$11.538$	6.6.1397493.1	None	✓	✓			1445.2.a.l	$1$	$1$	\(-3\)	\(3\)	\(-6\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{5})q^{2}+(\beta _{1}-\beta _{4})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
1445.2.a.n	$1445$	$2$	1445.a	1.a	$1$	$6$	$6$	$11.538$	6.6.7718912.1	None	✓				85.2.e.a	$1$	$1$	\(2\)	\(-4\)	\(-6\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1445.2.a.o	$1445$	$2$	1445.a	1.a	$1$	$6$	$6$	$11.538$	6.6.7718912.1	None	✓				85.2.e.a	$1$	$0$	\(2\)	\(4\)	\(6\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1445.2.a.p	$1445$	$2$	1445.a	1.a	$1$	$12$	$12$	$11.538$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		85.2.l.a	$1$	$1$	\(-4\)	\(-8\)	\(12\)	\(-16\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(1+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
1445.2.a.q	$1445$	$2$	1445.a	1.a	$1$	$12$	$12$	$11.538$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				85.2.l.a	$1$	$0$	\(-4\)	\(8\)	\(-12\)	\(16\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(1+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
1445.2.a.r	$1445$	$2$	1445.a	1.a	$1$	$12$	$12$	$11.538$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			1445.2.a.r	$1$	$0$	\(3\)	\(-3\)	\(-12\)	\(-6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
1445.2.a.s	$1445$	$2$	1445.a	1.a	$1$	$12$	$12$	$11.538$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		1445.2.a.r	$1$	$0$	\(3\)	\(3\)	\(12\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1445))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1445)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 2}\)