Space of modular forms of level 195, weight 2, and Character 195.bb

• Label: 195.2.bb
• Level: $195$
• Weight: $2$
• Character orbit: 195.bb
• Rep. character: $\chi_{195}(121,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $3$
• Sturm bound: $56$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(56\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(195, [\chi])\).

	Total	New	Old
Modular forms	64	20	44
Cusp forms	48	20	28
Eisenstein series	16	0	16

Trace form

20 * q - 2 * q^3 + 12 * q^4 + 6 * q^7 - 10 * q^9 + 4 * q^10 - 8 * q^12 - 2 * q^13 - 8 * q^14 - 8 * q^16 - 12 * q^17 - 12 * q^19 - 24 * q^20 + 12 * q^22 - 4 * q^23 - 20 * q^25 - 32 * q^26 + 4 * q^27 - 12 * q^28 + 8 * q^29 + 4 * q^30 + 60 * q^32 - 4 * q^35 + 12 * q^36 - 12 * q^37 - 4 * q^39 + 24 * q^40 - 20 * q^42 + 18 * q^43 + 72 * q^46 - 24 * q^48 + 24 * q^51 + 36 * q^52 - 32 * q^53 - 8 * q^55 + 16 * q^56 - 24 * q^58 + 30 * q^61 - 52 * q^62 - 6 * q^63 - 16 * q^64 + 20 * q^65 - 24 * q^66 - 30 * q^67 + 24 * q^68 - 4 * q^69 + 48 * q^71 - 4 * q^74 + 2 * q^75 - 48 * q^76 + 40 * q^77 - 8 * q^78 + 20 * q^79 - 10 * q^81 - 16 * q^82 + 36 * q^84 - 16 * q^87 + 8 * q^88 + 24 * q^89 - 8 * q^90 - 26 * q^91 + 8 * q^92 - 6 * q^93 + 24 * q^94 - 8 * q^95 - 18 * q^97 - 96 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(195, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
195.2.bb.a	$195$	$2$	195.bb	13.e	$6$	$4$	$2$	$1.557$	\(\Q(\zeta_{12})\)	None		✓			195.2.bb.a	$2$	$1$	\(-6\)	\(-2\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
195.2.bb.b	$195$	$2$	195.bb	13.e	$6$	$8$	$4$	$1.557$	8.0.191102976.5	None		✓			195.2.bb.b	$2$	$0$	\(0\)	\(4\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(1-\beta _{4}+\cdots)q^{3}+\cdots\)
195.2.bb.c	$195$	$2$	195.bb	13.e	$6$	$8$	$4$	$1.557$	8.0.56070144.2	None		✓			195.2.bb.c	$2$	$0$	\(6\)	\(-4\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(195, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(195, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)