Space of modular forms of level 196, weight 2, and Character 196.e

• Label: 196.2.e
• Level: $196$
• Weight: $2$
• Character orbit: 196.e
• Rep. character: $\chi_{196}(165,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $56$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(56\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(196, [\chi])\).

	Total	New	Old
Modular forms	80	6	74
Cusp forms	32	6	26
Eisenstein series	48	0	48

Trace form

6 * q + q^3 + 3 * q^5 - 8 * q^9 - 5 * q^11 - 4 * q^13 - 10 * q^15 + 3 * q^17 - q^19 + 5 * q^23 + 2 * q^25 + 10 * q^27 + 20 * q^29 - 7 * q^31 - 3 * q^33 + 17 * q^37 + 22 * q^39 - 12 * q^41 - 24 * q^43 - 6 * q^45 - 9 * q^47 + 5 * q^51 - 23 * q^53 + 18 * q^55 - 34 * q^57 + 9 * q^59 - q^61 - 18 * q^65 + 7 * q^67 - 6 * q^69 - q^73 + 4 * q^75 - 3 * q^79 - 3 * q^81 - 24 * q^83 + 26 * q^85 - 6 * q^87 + 15 * q^89 + 7 * q^93 - 5 * q^95 + 20 * q^97 + 92 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(196, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
196.2.e.a	$196$	$2$	196.e	7.c	$3$	$2$	$1$	$1.565$	\(\Q(\sqrt{-3}) \)	None					28.2.e.a	$2$	$0$	\(0\)	\(1\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots\)
196.2.e.b	$196$	$2$	196.e	7.c	$3$	$4$	$2$	$1.565$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓	✓		196.2.a.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(196, [\chi])\) into lower level spaces

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