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

• Label: 196.2.d
• Level: $196$
• Weight: $2$
• Character orbit: 196.d
• Rep. character: $\chi_{196}(195,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $56$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(56\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	36	24	12
Cusp forms	20	16	4
Eisenstein series	16	8	8

Trace form

16 * q + 4 * q^4 - 12 * q^8 + 12 * q^9 + 4 * q^16 - 20 * q^18 + 12 * q^22 - 4 * q^25 - 16 * q^29 - 28 * q^30 + 20 * q^32 - 20 * q^36 - 20 * q^37 + 16 * q^44 - 4 * q^46 - 4 * q^50 + 28 * q^53 - 4 * q^57 - 8 * q^58 + 32 * q^60 - 20 * q^64 + 8 * q^65 - 4 * q^72 - 12 * q^74 + 32 * q^78 - 56 * q^81 - 20 * q^85 + 72 * q^86 - 72 * q^88 + 64 * q^92 - 44 * q^93

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.d.a	$196$	$2$	196.d	28.d	$2$	$4$	$4$	$1.565$	4.0.2048.2	\(\Q(\sqrt{-1}) \)		✓			196.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$7$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}-2\beta _{2}q^{8}+\cdots\)
196.2.d.b	$196$	$2$	196.d	28.d	$2$	$4$	$4$	$1.565$	\(\Q(\zeta_{12})\)	None					28.2.f.a	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_1+1)q^{2}+\beta_{3} q^{3}+2\beta_1 q^{4}+\cdots\)
196.2.d.c	$196$	$2$	196.d	28.d	$2$	$8$	$8$	$1.565$	8.0.\(\cdots\).10	None		✓	✓		196.2.d.c	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{5})q^{2}+(-2\beta _{1}-\beta _{7})q^{3}+\cdots\)

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

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