Space of modular forms of level 1445, weight 4, and trivial character

• Label: 1445.4.a
• Level: $1445$
• Weight: $4$
• Character orbit: 1445.a
• Rep. character: $\chi_{1445}(1,\cdot)$
• Character field: $\Q$
• Dimension: $271$
• Newform subspaces: $26$
• Sturm bound: $612$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1445.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(612\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1445))\).

	Total	New	Old
Modular forms	478	271	207
Cusp forms	442	271	171
Eisenstein series	36	0	36

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
\(+\)	\(+\)	\(+\)		\(126\)	\(72\)	\(54\)		\(117\)	\(72\)	\(45\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(-\)		\(113\)	\(64\)	\(49\)		\(104\)	\(64\)	\(40\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)		\(117\)	\(63\)	\(54\)		\(108\)	\(63\)	\(45\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)		\(122\)	\(72\)	\(50\)		\(113\)	\(72\)	\(41\)		\(9\)	\(0\)	\(9\)
Plus space		\(+\)		\(248\)	\(144\)	\(104\)		\(230\)	\(144\)	\(86\)		\(18\)	\(0\)	\(18\)
Minus space		\(-\)		\(230\)	\(127\)	\(103\)		\(212\)	\(127\)	\(85\)		\(18\)	\(0\)	\(18\)

Trace form

271 * q - 2 * q^3 + 1100 * q^4 - 5 * q^5 - 60 * q^6 + 6 * q^7 + 48 * q^8 + 2499 * q^9 - 40 * q^10 - 20 * q^11 + 188 * q^12 + 30 * q^13 + 260 * q^14 + 10 * q^15 + 4276 * q^16 + 100 * q^18 + 344 * q^19 - 80 * q^20 + 220 * q^21 + 336 * q^22 - 22 * q^23 - 944 * q^24 + 6775 * q^25 + 308 * q^26 - 476 * q^27 + 500 * q^28 - 506 * q^29 + 160 * q^30 - 28 * q^31 + 484 * q^32 - 160 * q^33 + 290 * q^35 + 11040 * q^36 + 522 * q^37 - 824 * q^38 + 1132 * q^39 - 240 * q^40 - 414 * q^41 - 2436 * q^42 + 678 * q^43 - 892 * q^44 + 275 * q^45 + 848 * q^46 + 1258 * q^47 + 2432 * q^48 + 12499 * q^49 - 796 * q^52 + 822 * q^53 - 2300 * q^54 + 160 * q^55 + 1928 * q^56 - 1176 * q^57 + 1092 * q^58 + 416 * q^59 - 900 * q^60 + 610 * q^61 + 1304 * q^62 - 2114 * q^63 + 16328 * q^64 - 450 * q^65 + 556 * q^66 - 2158 * q^67 + 1900 * q^69 + 240 * q^70 + 220 * q^71 + 7076 * q^72 + 230 * q^73 + 60 * q^74 - 50 * q^75 + 520 * q^76 + 192 * q^77 + 2036 * q^78 - 1008 * q^79 + 19939 * q^81 - 2948 * q^82 + 230 * q^83 + 4636 * q^84 - 1912 * q^86 + 2668 * q^87 + 1244 * q^88 - 3962 * q^89 - 2620 * q^90 + 1380 * q^91 + 192 * q^92 - 1744 * q^93 - 3040 * q^94 - 1020 * q^95 - 2172 * q^96 + 1142 * q^97 - 380 * q^98 + 1300 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1445))\) 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
1445.4.a.a	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	\(\Q\)	None	✓				5.4.a.a	$1$	$1$	\(-4\)	\(-2\)	\(5\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-2q^{3}+8q^{4}+5q^{5}+8q^{6}+\cdots\)
1445.4.a.b	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	\(\Q\)	None	✓	✓			1445.4.a.b	$1$	$0$	\(-3\)	\(-2\)	\(-5\)	\(-5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}-2q^{3}+q^{4}-5q^{5}+6q^{6}+\cdots\)
1445.4.a.c	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	\(\Q\)	None	✓	✓			1445.4.a.b	$1$	$0$	\(-3\)	\(2\)	\(5\)	\(5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+2q^{3}+q^{4}+5q^{5}-6q^{6}+\cdots\)
1445.4.a.d	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	\(\Q\)	None	✓				85.4.d.a	$1$	$2$	\(-1\)	\(-8\)	\(-5\)	\(-14\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-8q^{3}-7q^{4}-5q^{5}+8q^{6}+\cdots\)
1445.4.a.e	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	\(\Q\)	None	✓				85.4.d.a	$1$	$1$	\(-1\)	\(8\)	\(5\)	\(14\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+8q^{3}-7q^{4}+5q^{5}-8q^{6}+\cdots\)
1445.4.a.f	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	\(\Q\)	None	✓				85.4.a.c	$1$	$0$	\(3\)	\(-10\)	\(-5\)	\(22\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}-10q^{3}+q^{4}-5q^{5}-30q^{6}+\cdots\)
1445.4.a.g	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	\(\Q\)	None	✓				85.4.a.b	$1$	$1$	\(3\)	\(5\)	\(5\)	\(22\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+5q^{3}+q^{4}+5q^{5}+15q^{6}+\cdots\)
1445.4.a.h	$1445$	$4$	1445.a	1.a	$1$	$1$	$1$	$85.258$	\(\Q\)	None	✓				85.4.a.a	$1$	$0$	\(3\)	\(7\)	\(-5\)	\(22\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+7q^{3}+q^{4}-5q^{5}+21q^{6}+\cdots\)
1445.4.a.i	$1445$	$4$	1445.a	1.a	$1$	$2$	$2$	$85.258$	\(\Q(\sqrt{3}) \)	None	✓				85.4.a.d	$1$	$0$	\(-4\)	\(2\)	\(-10\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{2}+(1-\beta )q^{3}+(-1-4\beta )q^{4}+\cdots\)
1445.4.a.j	$1445$	$4$	1445.a	1.a	$1$	$3$	$3$	$85.258$	3.3.1304.1	None	✓				85.4.a.e	$1$	$1$	\(-6\)	\(4\)	\(15\)	\(-8\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
1445.4.a.k	$1445$	$4$	1445.a	1.a	$1$	$3$	$3$	$85.258$	3.3.568.1	None	✓				85.4.a.f	$1$	$1$	\(3\)	\(-9\)	\(15\)	\(-34\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2})q^{2}+(-4+3\beta _{1})q^{3}+\cdots\)
1445.4.a.l	$1445$	$4$	1445.a	1.a	$1$	$5$	$5$	$85.258$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				85.4.a.g	$1$	$0$	\(2\)	\(1\)	\(-25\)	\(-10\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(6-2\beta _{1}+\beta _{3})q^{4}+\cdots\)
1445.4.a.m	$1445$	$4$	1445.a	1.a	$1$	$7$	$7$	$85.258$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			1445.4.a.m	$1$	$1$	\(-3\)	\(0\)	\(-35\)	\(11\)		$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1445.4.a.n	$1445$	$4$	1445.a	1.a	$1$	$7$	$7$	$85.258$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			1445.4.a.m	$1$	$1$	\(-3\)	\(0\)	\(35\)	\(-11\)		$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1445.4.a.o	$1445$	$4$	1445.a	1.a	$1$	$8$	$8$	$85.258$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				85.4.d.b	$1$	$1$	\(-1\)	\(-18\)	\(40\)	\(-38\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-2-\beta _{3})q^{3}+(6+\beta _{2})q^{4}+\cdots\)
1445.4.a.p	$1445$	$4$	1445.a	1.a	$1$	$8$	$8$	$85.258$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				85.4.d.b	$1$	$0$	\(-1\)	\(18\)	\(-40\)	\(38\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{3})q^{3}+(6+\beta _{2})q^{4}+\cdots\)
1445.4.a.q	$1445$	$4$	1445.a	1.a	$1$	$8$	$8$	$85.258$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			1445.4.a.q	$1$	$0$	\(4\)	\(-2\)	\(40\)	\(32\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(6+\beta _{2})q^{4}+\cdots\)
1445.4.a.r	$1445$	$4$	1445.a	1.a	$1$	$8$	$8$	$85.258$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			1445.4.a.q	$1$	$0$	\(4\)	\(2\)	\(-40\)	\(-32\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-\beta _{6}q^{3}+(6+\beta _{2})q^{4}+\cdots\)
1445.4.a.s	$1445$	$4$	1445.a	1.a	$1$	$18$	$18$	$85.258$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓				85.4.e.a	$1$	$1$	\(-4\)	\(-12\)	\(90\)	\(-56\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{7})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
1445.4.a.t	$1445$	$4$	1445.a	1.a	$1$	$18$	$18$	$85.258$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓				85.4.e.a	$1$	$0$	\(-4\)	\(12\)	\(-90\)	\(56\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{7})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
1445.4.a.u	$1445$	$4$	1445.a	1.a	$1$	$21$	$21$	$85.258$		None	✓	✓	✓		1445.4.a.u	$1$	$1$	\(-6\)	\(-18\)	\(105\)	\(-42\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
1445.4.a.v	$1445$	$4$	1445.a	1.a	$1$	$21$	$21$	$85.258$		None	✓	✓			1445.4.a.u	$1$	$1$	\(-6\)	\(18\)	\(-105\)	\(42\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
1445.4.a.w	$1445$	$4$	1445.a	1.a	$1$	$27$	$27$	$85.258$		None	✓	✓	✓		1445.4.a.w	$1$	$0$	\(6\)	\(-18\)	\(-135\)	\(-42\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
1445.4.a.x	$1445$	$4$	1445.a	1.a	$1$	$27$	$27$	$85.258$		None	✓	✓			1445.4.a.w	$1$	$0$	\(6\)	\(18\)	\(135\)	\(42\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
1445.4.a.y	$1445$	$4$	1445.a	1.a	$1$	$36$	$36$	$85.258$		None	✓		✓		85.4.l.a	$1$	$1$	\(8\)	\(-24\)	\(-180\)	\(-112\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
1445.4.a.z	$1445$	$4$	1445.a	1.a	$1$	$36$	$36$	$85.258$		None	✓		✓		85.4.l.a	$1$	$0$	\(8\)	\(24\)	\(180\)	\(112\)		$-$	$-$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1445))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1445)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 2}\)