Space of modular forms of level 121, weight 6, and trivial character

• Label: 121.6.a
• Level: $121$
• Weight: $6$
• Character orbit: 121.a
• Rep. character: $\chi_{121}(1,\cdot)$
• Character field: $\Q$
• Dimension: $41$
• Newform subspaces: $9$
• Sturm bound: $66$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(66\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(121))\).

	Total	New	Old
Modular forms	61	50	11
Cusp forms	49	41	8
Eisenstein series	12	9	3

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

\(11\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(29\)	\(23\)	\(6\)		\(23\)	\(19\)	\(4\)		\(6\)	\(4\)	\(2\)
\(-\)		\(32\)	\(27\)	\(5\)		\(26\)	\(22\)	\(4\)		\(6\)	\(5\)	\(1\)

Trace form

41 * q + 4 * q^2 - 18 * q^3 + 572 * q^4 - 34 * q^5 + 146 * q^6 - 94 * q^7 + 372 * q^8 + 2891 * q^9 + 338 * q^10 - 1178 * q^12 + 662 * q^13 + 1680 * q^14 - 2474 * q^15 + 5564 * q^16 - 1772 * q^17 + 3634 * q^18 - 996 * q^19 - 580 * q^20 + 1058 * q^21 + 1386 * q^23 + 14628 * q^24 + 20099 * q^25 - 20656 * q^26 - 2118 * q^27 - 23552 * q^28 + 8850 * q^29 - 1510 * q^30 + 6142 * q^31 + 17528 * q^32 - 21710 * q^34 + 24418 * q^35 + 34750 * q^36 - 35398 * q^37 + 9182 * q^38 - 10660 * q^39 + 18924 * q^40 - 4466 * q^41 + 31284 * q^42 + 30234 * q^43 - 3076 * q^45 + 31642 * q^46 + 20984 * q^47 - 86174 * q^48 - 5135 * q^49 - 52126 * q^50 + 33014 * q^51 + 16936 * q^52 - 37996 * q^53 - 3154 * q^54 + 34332 * q^56 - 25920 * q^57 + 27712 * q^58 + 26138 * q^59 + 21212 * q^60 - 1506 * q^61 - 5798 * q^62 + 12676 * q^63 + 19532 * q^64 - 14144 * q^65 + 34134 * q^67 + 23576 * q^68 - 33266 * q^69 + 133892 * q^70 - 86822 * q^71 + 98496 * q^72 - 17350 * q^73 - 105042 * q^74 + 50084 * q^75 - 110064 * q^76 - 139520 * q^78 - 190286 * q^79 - 228224 * q^80 + 190313 * q^81 + 243474 * q^82 + 246642 * q^83 - 346016 * q^84 + 117074 * q^85 - 169034 * q^86 - 61992 * q^87 + 77606 * q^89 - 102056 * q^90 - 321724 * q^91 + 460740 * q^92 - 382734 * q^93 + 103600 * q^94 + 14904 * q^95 - 344 * q^96 - 146250 * q^97 - 70308 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(121))\) 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
121.6.a.a	$121$	$6$	121.a	1.a	$1$	$1$	$1$	$19.406$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	✓			121.6.a.a	$2$	$1$	\(0\)	\(-31\)	\(57\)	\(0\)		$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-31q^{3}-2^{5}q^{4}+57q^{5}+718q^{9}+\cdots\)
121.6.a.b	$121$	$6$	121.a	1.a	$1$	$1$	$1$	$19.406$	\(\Q\)	None	✓				11.6.a.a	$1$	$0$	\(4\)	\(-15\)	\(-19\)	\(-10\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}-15q^{3}-2^{4}q^{4}-19q^{5}-60q^{6}+\cdots\)
121.6.a.c	$121$	$6$	121.a	1.a	$1$	$2$	$2$	$19.406$	\(\Q(\sqrt{38}) \)	None	✓	✓			121.6.a.c	$2$	$1$	\(0\)	\(14\)	\(-38\)	\(0\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+7q^{3}+6q^{4}-19q^{5}+7\beta q^{6}+\cdots\)
121.6.a.d	$121$	$6$	121.a	1.a	$1$	$3$	$3$	$19.406$	3.3.54492.1	None	✓				11.6.a.b	$1$	$0$	\(0\)	\(34\)	\(24\)	\(-84\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(11+\beta _{1}-\beta _{2})q^{3}+(30-6\beta _{1}+\cdots)q^{4}+\cdots\)
121.6.a.e	$121$	$6$	121.a	1.a	$1$	$5$	$5$	$19.406$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			121.6.a.e	$1$	$0$	\(-4\)	\(10\)	\(29\)	\(102\)		$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2+\beta _{1}+\beta _{2})q^{3}+\cdots\)
121.6.a.f	$121$	$6$	121.a	1.a	$1$	$5$	$5$	$19.406$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			121.6.a.e	$1$	$0$	\(4\)	\(10\)	\(29\)	\(-102\)		$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2+\beta _{1}+\beta _{2})q^{3}+(21+\cdots)q^{4}+\cdots\)
121.6.a.g	$121$	$6$	121.a	1.a	$1$	$8$	$8$	$19.406$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				11.6.c.a	$1$	$1$	\(-8\)	\(-12\)	\(70\)	\(-292\)		$+$	$+$	$2^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-2-\beta _{6})q^{3}+(11+\cdots)q^{4}+\cdots\)
121.6.a.h	$121$	$6$	121.a	1.a	$1$	$8$	$8$	$19.406$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			121.6.a.h	$2$	$1$	\(0\)	\(-16\)	\(-256\)	\(0\)		$+$	$+$	$2^{4}\cdot 11$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-2+\beta _{6})q^{3}+(19-\beta _{2}+\cdots)q^{4}+\cdots\)
121.6.a.i	$121$	$6$	121.a	1.a	$1$	$8$	$8$	$19.406$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		11.6.c.a	$1$	$0$	\(8\)	\(-12\)	\(70\)	\(292\)		$-$	$-$	$2^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-2-\beta _{6})q^{3}+(11-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(121))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(121)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)