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

• Label: 195.2.c
• Level: $195$
• Weight: $2$
• Character orbit: 195.c
• Rep. character: $\chi_{195}(79,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $56$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(56\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	32	12	20
Cusp forms	24	12	12
Eisenstein series	8	0	8

Trace form

12 * q - 8 * q^4 - 4 * q^5 - 12 * q^9 + 4 * q^10 + 8 * q^11 - 24 * q^14 - 4 * q^15 + 8 * q^16 - 8 * q^19 + 28 * q^20 + 8 * q^21 + 4 * q^25 + 4 * q^30 + 16 * q^31 - 40 * q^34 + 8 * q^35 + 8 * q^36 - 8 * q^39 + 36 * q^40 - 8 * q^41 - 40 * q^44 + 4 * q^45 - 24 * q^46 - 32 * q^49 + 40 * q^50 - 12 * q^51 + 4 * q^55 - 24 * q^59 + 12 * q^60 + 4 * q^61 + 48 * q^64 + 4 * q^65 - 16 * q^66 + 20 * q^69 + 56 * q^70 + 8 * q^71 - 24 * q^74 + 8 * q^75 + 16 * q^76 - 4 * q^79 - 20 * q^80 + 12 * q^81 - 32 * q^84 - 8 * q^85 - 8 * q^89 - 4 * q^90 + 12 * q^91 + 24 * q^94 - 56 * q^95 - 40 * q^96 - 8 * 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.c.a	$195$	$2$	195.c	5.b	$2$	$2$	$2$	$1.557$	\(\Q(\sqrt{-1}) \)	None		✓			195.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 q^{4}+(2 i-1)q^{5}+i q^{7}+\cdots\)
195.2.c.b	$195$	$2$	195.c	5.b	$2$	$10$	$10$	$1.557$	10.0.\(\cdots\).1	None		✓	✓		195.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)

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

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