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

• Label: 195.2.i
• Level: $195$
• Weight: $2$
• Character orbit: 195.i
• Rep. character: $\chi_{195}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $56$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(56\)
Trace bound:			\(4\)
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 - 2 * q^7 - 10 * q^9 + 4 * q^10 - 8 * q^11 - 8 * q^12 + 10 * q^13 + 8 * q^14 - 24 * q^16 + 4 * q^17 - 8 * q^20 + 12 * q^21 + 4 * q^22 - 12 * q^23 + 24 * q^24 + 20 * q^25 - 32 * q^26 - 4 * q^27 - 36 * q^28 + 8 * q^29 + 4 * q^30 - 12 * q^31 + 20 * q^32 + 16 * q^34 - 4 * q^35 - 12 * q^36 + 8 * q^37 + 80 * q^38 + 4 * q^39 - 24 * q^40 + 32 * q^41 - 4 * q^42 + 2 * q^43 - 8 * q^44 + 8 * q^46 - 48 * q^47 - 8 * q^48 - 28 * q^49 + 8 * q^51 + 28 * q^52 - 64 * q^53 + 16 * q^55 - 8 * q^56 - 48 * q^57 - 8 * q^58 - 16 * q^59 + 18 * q^61 + 12 * q^62 - 2 * q^63 - 16 * q^64 + 4 * q^65 + 40 * q^66 + 6 * q^67 + 72 * q^68 + 4 * q^69 + 16 * q^70 + 8 * q^71 + 52 * q^73 + 44 * q^74 + 2 * q^75 - 8 * q^76 - 40 * q^77 + 16 * q^78 + 12 * q^79 - 32 * q^80 - 10 * q^81 + 8 * q^82 - 8 * q^83 - 12 * q^84 - 48 * q^86 + 32 * q^87 + 16 * q^88 - 48 * q^89 - 8 * q^90 - 10 * q^91 + 104 * q^92 - 6 * q^93 - 56 * q^94 - 8 * q^95 - 56 * q^96 - 26 * q^97 - 72 * q^98 + 16 * q^99

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.i.a	$195$	$2$	195.i	13.c	$3$	$2$	$1$	$1.557$	\(\Q(\sqrt{-3}) \)	None		✓			195.2.i.a	$2$	$1$	\(-2\)	\(-1\)	\(-2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
195.2.i.b	$195$	$2$	195.i	13.c	$3$	$2$	$1$	$1.557$	\(\Q(\sqrt{-3}) \)	None		✓			195.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}-q^{5}+\zeta_{6}q^{7}+\cdots\)
195.2.i.c	$195$	$2$	195.i	13.c	$3$	$4$	$2$	$1.557$	\(\Q(\zeta_{12})\)	None		✓			195.2.i.c	$2$	$0$	\(2\)	\(-2\)	\(4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta_{2}+\beta_1)q^{2}-\beta_1 q^{3}+(2\beta_{3}-2\beta_{2}+2\beta_1-2)q^{4}+\cdots\)
195.2.i.d	$195$	$2$	195.i	13.c	$3$	$6$	$3$	$1.557$	6.0.1714608.1	None		✓			195.2.i.d	$2$	$0$	\(0\)	\(3\)	\(6\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}+\beta _{5})q^{2}+(1+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
195.2.i.e	$195$	$2$	195.i	13.c	$3$	$6$	$3$	$1.557$	6.0.591408.1	None		✓			195.2.i.e	$2$	$0$	\(0\)	\(3\)	\(-6\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{2}+(1-\beta _{4})q^{3}+(\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)

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

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