Space of modular forms of level 196, weight 10, and Character 196.e

• Label: 196.10.e
• Level: $196$
• Weight: $10$
• Character orbit: 196.e
• Rep. character: $\chi_{196}(165,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $60$
• Newform subspaces: $9$
• Sturm bound: $280$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	196.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(280\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(196, [\chi])\).

	Total	New	Old
Modular forms	528	60	468
Cusp forms	480	60	420
Eisenstein series	48	0	48

Trace form

60 * q + 966 * q^5 - 215424 * q^9 + 63052 * q^11 - 103432 * q^13 + 959992 * q^15 + 402234 * q^17 + 519960 * q^19 + 1757156 * q^23 - 13615872 * q^25 + 7641648 * q^27 - 9866440 * q^29 + 1040564 * q^31 - 5260178 * q^33 + 34115442 * q^37 - 39036160 * q^39 - 34183128 * q^41 + 51940600 * q^43 + 17040100 * q^45 + 26858748 * q^47 - 60409564 * q^51 + 159587194 * q^53 - 54952184 * q^55 - 307905252 * q^57 - 31298904 * q^59 + 155592542 * q^61 - 69202332 * q^65 + 248020080 * q^67 + 249902212 * q^69 - 1047247824 * q^71 + 549596530 * q^73 + 647801672 * q^75 - 99736004 * q^79 - 2204076610 * q^81 - 989338224 * q^83 + 61477396 * q^85 + 860715296 * q^87 + 1746541986 * q^89 - 3341795282 * q^93 - 2000289932 * q^95 - 2306715320 * q^97 - 3824328008 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(196, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
196.10.e.a	$196$	$10$	196.e	7.c	$3$	$2$	$1$	$100.947$	\(\Q(\sqrt{-3}) \)	None					4.10.a.a	$2$	$0$	\(0\)	\(-228\)	\(666\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-228+228\zeta_{6})q^{3}+666\zeta_{6}q^{5}+\cdots\)
196.10.e.b	$196$	$10$	196.e	7.c	$3$	$2$	$1$	$100.947$	\(\Q(\sqrt{-3}) \)	None					4.10.a.a	$2$	$0$	\(0\)	\(228\)	\(-666\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(228-228\zeta_{6})q^{3}-666\zeta_{6}q^{5}-32301\zeta_{6}q^{9}+\cdots\)
196.10.e.c	$196$	$10$	196.e	7.c	$3$	$4$	$2$	$100.947$	\(\Q(\sqrt{-3}, \sqrt{4561})\)	None					28.10.a.a	$2$	$0$	\(0\)	\(-224\)	\(1596\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-112\beta _{1}+\beta _{2})q^{3}+(798-798\beta _{1}+\cdots)q^{5}+\cdots\)
196.10.e.d	$196$	$10$	196.e	7.c	$3$	$4$	$2$	$100.947$	\(\Q(\sqrt{-3}, \sqrt{11209})\)	None					28.10.a.b	$2$	$0$	\(0\)	\(-70\)	\(1554\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-35\beta _{1}-\beta _{2})q^{3}+(777-777\beta _{1}+\cdots)q^{5}+\cdots\)
196.10.e.e	$196$	$10$	196.e	7.c	$3$	$4$	$2$	$100.947$	\(\Q(\sqrt{-3}, \sqrt{11209})\)	None					28.10.a.b	$2$	$0$	\(0\)	\(70\)	\(-1554\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(35\beta _{1}-\beta _{2})q^{3}+(-777+777\beta _{1}+\cdots)q^{5}+\cdots\)
196.10.e.f	$196$	$10$	196.e	7.c	$3$	$4$	$2$	$100.947$	\(\Q(\sqrt{-3}, \sqrt{4561})\)	None					28.10.a.a	$2$	$0$	\(0\)	\(224\)	\(-1596\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(112\beta _{1}-\beta _{2})q^{3}+(-798+798\beta _{1}+\cdots)q^{5}+\cdots\)
196.10.e.g	$196$	$10$	196.e	7.c	$3$	$8$	$4$	$100.947$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓			196.10.a.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}-\beta _{3})q^{3}+(3\beta _{2}+\beta _{4})q^{5}+(-5057\beta _{1}+\cdots)q^{9}+\cdots\)
196.10.e.h	$196$	$10$	196.e	7.c	$3$	$12$	$6$	$100.947$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					28.10.e.a	$2$	$0$	\(0\)	\(0\)	\(966\)	\(0\)	$2^{28}\cdot 3^{5}\cdot 7^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}+\beta _{3})q^{3}+(161-161\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
196.10.e.i	$196$	$10$	196.e	7.c	$3$	$20$	$10$	$100.947$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		196.10.a.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{44}\cdot 3^{8}\cdot 7^{24}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{13}q^{3}+(-5\beta _{10}-5\beta _{11}+3\beta _{12}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(196, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(196, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)