Space of modular forms of level 182, weight 4, and trivial character

• Label: 182.4.a
• Level: $182$
• Weight: $4$
• Character orbit: 182.a
• Rep. character: $\chi_{182}(1,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $10$
• Sturm bound: $112$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	182.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(112\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(182))\).

	Total	New	Old
Modular forms	88	18	70
Cusp forms	80	18	62
Eisenstein series	8	0	8

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

\(2\)	\(7\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(14\)	\(3\)	\(11\)		\(13\)	\(3\)	\(10\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)		\(9\)	\(2\)	\(7\)		\(8\)	\(2\)	\(6\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(10\)	\(2\)	\(8\)		\(9\)	\(2\)	\(7\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(11\)	\(3\)	\(8\)		\(10\)	\(3\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(10\)	\(1\)	\(9\)		\(9\)	\(1\)	\(8\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(11\)	\(3\)	\(8\)		\(10\)	\(3\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(11\)	\(3\)	\(8\)		\(10\)	\(3\)	\(7\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(12\)	\(1\)	\(11\)		\(11\)	\(1\)	\(10\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(47\)	\(12\)	\(35\)		\(43\)	\(12\)	\(31\)		\(4\)	\(0\)	\(4\)
Minus space			\(-\)		\(41\)	\(6\)	\(35\)		\(37\)	\(6\)	\(31\)		\(4\)	\(0\)	\(4\)

Trace form

18 * q - 4 * q^2 - 12 * q^3 + 72 * q^4 + 32 * q^5 + 40 * q^6 - 16 * q^8 + 270 * q^9 + 56 * q^11 - 48 * q^12 + 280 * q^15 + 288 * q^16 - 52 * q^17 + 76 * q^18 - 260 * q^19 + 128 * q^20 - 84 * q^21 - 216 * q^22 + 392 * q^23 + 160 * q^24 - 262 * q^25 + 264 * q^27 + 144 * q^29 + 48 * q^30 - 624 * q^31 - 64 * q^32 + 472 * q^33 + 360 * q^34 + 56 * q^35 + 1080 * q^36 + 516 * q^37 + 152 * q^38 - 540 * q^41 + 660 * q^43 + 224 * q^44 + 1528 * q^45 - 16 * q^46 + 504 * q^47 - 192 * q^48 + 882 * q^49 - 1244 * q^50 - 1056 * q^51 - 512 * q^53 + 16 * q^54 - 448 * q^55 - 1080 * q^57 - 1096 * q^58 + 1124 * q^59 + 1120 * q^60 - 752 * q^61 - 32 * q^62 - 224 * q^63 + 1152 * q^64 - 104 * q^65 - 768 * q^66 + 1848 * q^67 - 208 * q^68 - 4280 * q^69 + 728 * q^70 - 2432 * q^71 + 304 * q^72 - 724 * q^73 - 1152 * q^74 - 60 * q^75 - 1040 * q^76 - 312 * q^78 - 2568 * q^79 + 512 * q^80 + 1362 * q^81 + 2840 * q^82 - 2700 * q^83 - 336 * q^84 - 1784 * q^85 - 704 * q^86 - 3600 * q^87 - 864 * q^88 - 484 * q^89 - 2800 * q^90 - 182 * q^91 + 1568 * q^92 - 936 * q^93 - 2208 * q^94 - 6356 * q^95 + 640 * q^96 + 4948 * q^97 - 196 * q^98 + 2360 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(182))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	13
182.4.a.a	$182$	$4$	182.a	1.a	$1$	$1$	$1$	$10.738$	\(\Q\)	None	✓	✓			182.4.a.a	$1$	$0$	\(-2\)	\(7\)	\(0\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+7q^{3}+4q^{4}-14q^{6}+7q^{7}+\cdots\)
182.4.a.b	$182$	$4$	182.a	1.a	$1$	$1$	$1$	$10.738$	\(\Q\)	None	✓	✓	✓	✓	182.4.a.b	$1$	$1$	\(2\)	\(-8\)	\(3\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-8q^{3}+4q^{4}+3q^{5}-2^{4}q^{6}+\cdots\)
182.4.a.c	$182$	$4$	182.a	1.a	$1$	$1$	$1$	$10.738$	\(\Q\)	None	✓	✓	✓	✓	182.4.a.c	$1$	$1$	\(2\)	\(-2\)	\(-5\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-2q^{3}+4q^{4}-5q^{5}-4q^{6}+\cdots\)
182.4.a.d	$182$	$4$	182.a	1.a	$1$	$1$	$1$	$10.738$	\(\Q\)	None	✓	✓			182.4.a.d	$1$	$0$	\(2\)	\(5\)	\(16\)	\(7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+5q^{3}+4q^{4}+2^{4}q^{5}+10q^{6}+\cdots\)
182.4.a.e	$182$	$4$	182.a	1.a	$1$	$2$	$2$	$10.738$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓	✓	182.4.a.e	$1$	$1$	\(-4\)	\(-10\)	\(-8\)	\(14\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-5+3\beta )q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
182.4.a.f	$182$	$4$	182.a	1.a	$1$	$2$	$2$	$10.738$	\(\Q(\sqrt{1169}) \)	None	✓	✓	✓		182.4.a.f	$1$	$0$	\(-4\)	\(-8\)	\(5\)	\(14\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-4q^{3}+4q^{4}+(3-\beta )q^{5}+8q^{6}+\cdots\)
182.4.a.g	$182$	$4$	182.a	1.a	$1$	$2$	$2$	$10.738$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	182.4.a.g	$1$	$1$	\(-4\)	\(-4\)	\(6\)	\(-14\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-2+3\beta )q^{3}+4q^{4}+(3-\beta )q^{5}+\cdots\)
182.4.a.h	$182$	$4$	182.a	1.a	$1$	$2$	$2$	$10.738$	\(\Q(\sqrt{43}) \)	None	✓	✓	✓		182.4.a.h	$1$	$0$	\(4\)	\(2\)	\(4\)	\(14\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(1+\beta )q^{3}+4q^{4}+(2-\beta )q^{5}+\cdots\)
182.4.a.i	$182$	$4$	182.a	1.a	$1$	$3$	$3$	$10.738$	3.3.294825.1	None	✓	✓	✓	✓	182.4.a.i	$1$	$0$	\(-6\)	\(-1\)	\(13\)	\(-21\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(5-\beta _{1}+\beta _{2})q^{5}+\cdots\)
182.4.a.j	$182$	$4$	182.a	1.a	$1$	$3$	$3$	$10.738$	3.3.842136.1	None	✓	✓	✓	✓	182.4.a.j	$1$	$0$	\(6\)	\(7\)	\(-2\)	\(-21\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(2+\beta _{1})q^{3}+4q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(182))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(182)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)