Space of modular forms of level 3179, weight 2, and trivial character

• Label: 3179.2.a
• Level: $3179$
• Weight: $2$
• Character orbit: 3179.a
• Rep. character: $\chi_{3179}(1,\cdot)$
• Character field: $\Q$
• Dimension: $226$
• Newform subspaces: $35$
• Sturm bound: $612$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3179 = 11 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3179.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 35 \)
Sturm bound:			\(612\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3179))\).

	Total	New	Old
Modular forms	324	226	98
Cusp forms	289	226	63
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.

\(11\)	\(17\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(72\)	\(49\)	\(23\)		\(64\)	\(49\)	\(15\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)		\(90\)	\(63\)	\(27\)		\(81\)	\(63\)	\(18\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)		\(90\)	\(67\)	\(23\)		\(81\)	\(67\)	\(14\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)		\(72\)	\(47\)	\(25\)		\(63\)	\(47\)	\(16\)		\(9\)	\(0\)	\(9\)
Plus space		\(+\)		\(144\)	\(96\)	\(48\)		\(127\)	\(96\)	\(31\)		\(17\)	\(0\)	\(17\)
Minus space		\(-\)		\(180\)	\(130\)	\(50\)		\(162\)	\(130\)	\(32\)		\(18\)	\(0\)	\(18\)

Trace form

226 * q - q^2 + 3 * q^3 + 223 * q^4 - q^5 + 6 * q^6 + 6 * q^7 + 9 * q^8 + 231 * q^9 - 4 * q^10 + 2 * q^11 + 6 * q^12 + 2 * q^13 + 3 * q^15 + 213 * q^16 + 13 * q^18 + 16 * q^20 + 22 * q^21 + q^22 + 19 * q^23 + 16 * q^24 + 223 * q^25 - 18 * q^26 + 9 * q^27 + 2 * q^29 - 22 * q^30 + 15 * q^31 - 23 * q^32 - q^33 - 14 * q^35 + 225 * q^36 - 3 * q^37 + 12 * q^38 + 12 * q^39 - 26 * q^40 - 14 * q^41 - 32 * q^42 + 6 * q^43 + q^44 - 12 * q^45 - 2 * q^46 - 16 * q^47 + 4 * q^48 + 250 * q^49 - 37 * q^50 + 62 * q^52 - 8 * q^53 - 42 * q^54 - q^55 + 8 * q^56 + 8 * q^57 - 22 * q^58 - 23 * q^59 + 2 * q^60 + 2 * q^61 - 18 * q^62 - 48 * q^63 + 209 * q^64 - 24 * q^65 + 6 * q^66 + 17 * q^67 - 27 * q^69 + 36 * q^70 - 15 * q^71 + 29 * q^72 - 14 * q^73 - 40 * q^74 - 24 * q^75 + 24 * q^76 - 6 * q^77 - 20 * q^78 + 22 * q^79 + 102 * q^80 + 266 * q^81 + 18 * q^82 - 50 * q^83 + 72 * q^84 - 4 * q^86 - 16 * q^87 + 15 * q^88 - 19 * q^89 - 2 * q^90 + 16 * q^91 + 50 * q^92 - 27 * q^93 + 24 * q^94 - 28 * q^95 + 40 * q^96 - 5 * q^97 - 21 * q^98 + 11 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3179))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	17
3179.2.a.a	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	\(\Q\)	None	✓				11.2.a.a	$1$	$1$	\(-2\)	\(1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+2q^{7}+\cdots\)
3179.2.a.b	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	\(\Q\)	None	✓				187.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-3q^{5}-2q^{7}-2q^{9}+\cdots\)
3179.2.a.c	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	\(\Q\)	None	✓	✓			3179.2.a.c	$1$	$0$	\(2\)	\(-3\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-3q^{3}+2q^{4}-2q^{5}-6q^{6}+\cdots\)
3179.2.a.d	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	\(\Q\)	None	✓				187.2.a.b	$1$	$0$	\(2\)	\(0\)	\(-4\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-4q^{5}+5q^{7}-3q^{9}+\cdots\)
3179.2.a.e	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	\(\Q\)	None	✓	✓			3179.2.a.e	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}+2q^{7}-3q^{9}+\cdots\)
3179.2.a.f	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	\(\Q\)	None	✓	✓			3179.2.a.e	$1$	$1$	\(2\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}-2q^{7}-3q^{9}+\cdots\)
3179.2.a.g	$3179$	$2$	3179.a	1.a	$1$	$1$	$1$	$25.384$	\(\Q\)	None	✓	✓			3179.2.a.c	$1$	$0$	\(2\)	\(3\)	\(2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+2q^{4}+2q^{5}+6q^{6}+\cdots\)
3179.2.a.h	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	\(\Q(\sqrt{2}) \)	None	✓				187.2.e.a	$1$	$1$	\(-4\)	\(-4\)	\(0\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-2-\beta )q^{3}+2q^{4}-2\beta q^{5}+\cdots\)
3179.2.a.i	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	\(\Q(\sqrt{2}) \)	None	✓				187.2.e.a	$1$	$0$	\(-4\)	\(4\)	\(0\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(2-\beta )q^{3}+2q^{4}-2\beta q^{5}+\cdots\)
3179.2.a.j	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	\(\Q(\sqrt{2}) \)	None	✓	✓			3179.2.a.j	$1$	$0$	\(-2\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(-1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
3179.2.a.k	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	\(\Q(\sqrt{3}) \)	None	✓				187.2.a.c	$1$	$1$	\(-2\)	\(0\)	\(4\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+\beta q^{3}+(2-2\beta )q^{4}+\cdots\)
3179.2.a.l	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	\(\Q(\sqrt{2}) \)	None	✓	✓			3179.2.a.j	$1$	$0$	\(-2\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1+\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
3179.2.a.m	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	\(\Q(\sqrt{2}) \)	None	✓	✓			3179.2.a.m	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-2q^{3}+(1+2\beta )q^{5}-2\beta q^{6}+\cdots\)
3179.2.a.n	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	\(\Q(\sqrt{2}) \)	None	✓	✓			3179.2.a.m	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+2q^{3}+(-1-2\beta )q^{5}+2\beta q^{6}+\cdots\)
3179.2.a.o	$3179$	$2$	3179.a	1.a	$1$	$2$	$2$	$25.384$	\(\Q(\sqrt{17}) \)	None	✓				187.2.a.d	$1$	$1$	\(4\)	\(1\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(1-\beta )q^{3}+2q^{4}+(-1+\beta )q^{5}+\cdots\)
3179.2.a.p	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	3.3.788.1	None	✓	✓			3179.2.a.p	$1$	$1$	\(-3\)	\(-1\)	\(-1\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
3179.2.a.q	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	\(\Q(\zeta_{18})^+\)	None	✓	✓			3179.2.a.q	$1$	$1$	\(-3\)	\(0\)	\(-3\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{1}q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
3179.2.a.r	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	\(\Q(\zeta_{18})^+\)	None	✓	✓			3179.2.a.q	$1$	$1$	\(-3\)	\(0\)	\(3\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
3179.2.a.s	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	3.3.788.1	None	✓	✓			3179.2.a.p	$1$	$1$	\(-3\)	\(1\)	\(1\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
3179.2.a.t	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	3.3.148.1	None	✓				187.2.a.e	$1$	$0$	\(-2\)	\(3\)	\(7\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
3179.2.a.u	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	3.3.148.1	None	✓	✓			3179.2.a.u	$1$	$0$	\(1\)	\(-3\)	\(1\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
3179.2.a.v	$3179$	$2$	3179.a	1.a	$1$	$3$	$3$	$25.384$	3.3.148.1	None	✓	✓			3179.2.a.u	$1$	$0$	\(1\)	\(3\)	\(-1\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{2}+(1-\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
3179.2.a.w	$3179$	$2$	3179.a	1.a	$1$	$4$	$4$	$25.384$	4.4.33844.1	None	✓				187.2.a.f	$1$	$0$	\(1\)	\(-1\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
3179.2.a.x	$3179$	$2$	3179.a	1.a	$1$	$6$	$6$	$25.384$	6.6.1397493.1	None	✓	✓			3179.2.a.x	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{3}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{5})q^{3}+\cdots\)
3179.2.a.y	$3179$	$2$	3179.a	1.a	$1$	$6$	$6$	$25.384$	6.6.22313961.1	None	✓	✓			3179.2.a.y	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(\beta _{2}+\beta _{5})q^{4}+\cdots\)
3179.2.a.z	$3179$	$2$	3179.a	1.a	$1$	$6$	$6$	$25.384$	6.6.22313961.1	None	✓	✓			3179.2.a.y	$1$	$1$	\(0\)	\(0\)	\(6\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(\beta _{2}+\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)
3179.2.a.ba	$3179$	$2$	3179.a	1.a	$1$	$6$	$6$	$25.384$	6.6.1397493.1	None	✓	✓			3179.2.a.x	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{3}+\beta _{5})q^{2}+(\beta _{1}+\beta _{5})q^{3}+\cdots\)
3179.2.a.bb	$3179$	$2$	3179.a	1.a	$1$	$8$	$8$	$25.384$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				187.2.d.a	$1$	$1$	\(1\)	\(-2\)	\(-4\)	\(-5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
3179.2.a.bc	$3179$	$2$	3179.a	1.a	$1$	$8$	$8$	$25.384$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				187.2.d.a	$1$	$0$	\(1\)	\(2\)	\(4\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
3179.2.a.bd	$3179$	$2$	3179.a	1.a	$1$	$14$	$14$	$25.384$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓		✓		187.2.e.b	$1$	$1$	\(2\)	\(0\)	\(-8\)	\(-12\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
3179.2.a.be	$3179$	$2$	3179.a	1.a	$1$	$14$	$14$	$25.384$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓				187.2.e.b	$1$	$0$	\(2\)	\(0\)	\(8\)	\(12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
3179.2.a.bf	$3179$	$2$	3179.a	1.a	$1$	$27$	$27$	$25.384$		None	✓	✓			3179.2.a.bf	$1$	$0$	\(3\)	\(-3\)	\(-6\)	\(3\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
3179.2.a.bg	$3179$	$2$	3179.a	1.a	$1$	$27$	$27$	$25.384$		None	✓	✓	✓		3179.2.a.bf	$1$	$0$	\(3\)	\(3\)	\(6\)	\(-3\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
3179.2.a.bh	$3179$	$2$	3179.a	1.a	$1$	$28$	$28$	$25.384$		None	✓		✓		187.2.h.a	$1$	$1$	\(0\)	\(-8\)	\(-16\)	\(-12\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
3179.2.a.bi	$3179$	$2$	3179.a	1.a	$1$	$28$	$28$	$25.384$		None	✓		✓		187.2.h.a	$1$	$0$	\(0\)	\(8\)	\(16\)	\(12\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3179))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3179)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 2}\)