Space of modular forms of level 196, weight 5, and Character 196.h

• Label: 196.5.h
• Level: $196$
• Weight: $5$
• Character orbit: 196.h
• Rep. character: $\chi_{196}(117,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $26$
• Newform subspaces: $4$
• Sturm bound: $140$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	196.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(140\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(196, [\chi])\).

	Total	New	Old
Modular forms	248	26	222
Cusp forms	200	26	174
Eisenstein series	48	0	48

Trace form

26 * q - 9 * q^3 + 27 * q^5 + 376 * q^9 - 213 * q^11 + 1002 * q^15 + 1107 * q^17 + 747 * q^19 + 87 * q^23 - 668 * q^25 + 2028 * q^29 + 5355 * q^31 + 1863 * q^33 - 3697 * q^37 - 6508 * q^39 - 6460 * q^43 + 14418 * q^45 + 9747 * q^47 + 3405 * q^51 - 585 * q^53 + 23410 * q^57 + 2943 * q^59 - 4041 * q^61 + 3828 * q^65 - 3801 * q^67 + 420 * q^71 + 8703 * q^73 + 3438 * q^75 + 7631 * q^79 - 3009 * q^81 + 7122 * q^85 - 40014 * q^87 - 14985 * q^89 + 3129 * q^93 + 33177 * q^95 - 57748 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(196, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
196.5.h.a	$196$	$5$	196.h	7.d	$6$	$2$	$1$	$20.261$	\(\Q(\sqrt{-3}) \)	None					28.5.b.a	$2$	$0$	\(0\)	\(-12\)	\(36\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-4-4\zeta_{6})q^{3}+(24-12\zeta_{6})q^{5}+\cdots\)
196.5.h.b	$196$	$5$	196.h	7.d	$6$	$2$	$1$	$20.261$	\(\Q(\sqrt{-3}) \)	None					28.5.b.a	$2$	$0$	\(0\)	\(12\)	\(-36\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(4+4\zeta_{6})q^{3}+(-24+12\zeta_{6})q^{5}+\cdots\)
196.5.h.c	$196$	$5$	196.h	7.d	$6$	$6$	$3$	$20.261$	6.0.11337408.1	None					28.5.h.a	$2$	$0$	\(0\)	\(-9\)	\(27\)	\(0\)	$2^{2}\cdot 3^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\beta _{1}-\beta _{3})q^{3}+(3+3\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
196.5.h.d	$196$	$5$	196.h	7.d	$6$	$16$	$8$	$20.261$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		196.5.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 7^{16}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{10}q^{3}+(\beta _{8}-\beta _{9})q^{5}+(-44\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(196, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(196, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)