Space of modular forms of level 595, weight 2, and Character 595.ba

• Label: 595.2.ba
• Level: $595$
• Weight: $2$
• Character orbit: 595.ba
• Rep. character: $\chi_{595}(324,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $128$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 595 = 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	595.ba (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(595, [\chi])\).

	Total	New	Old
Modular forms	152	128	24
Cusp forms	136	128	8
Eisenstein series	16	0	16

Trace form

128 * q + 64 * q^4 - 24 * q^6 + 60 * q^9 - 2 * q^10 + 4 * q^11 - 16 * q^14 - 24 * q^15 - 64 * q^16 - 12 * q^19 - 24 * q^20 - 12 * q^21 - 36 * q^24 - 8 * q^25 + 4 * q^26 + 40 * q^29 - 2 * q^30 + 16 * q^34 + 14 * q^35 + 64 * q^36 - 4 * q^39 + 20 * q^40 - 72 * q^41 + 12 * q^44 + 36 * q^45 - 48 * q^46 - 28 * q^49 - 44 * q^50 - 64 * q^54 + 36 * q^55 + 44 * q^56 + 16 * q^59 - 2 * q^60 + 44 * q^61 - 80 * q^64 - 2 * q^65 - 76 * q^66 - 40 * q^69 + 14 * q^70 - 8 * q^74 + 6 * q^75 + 80 * q^76 - 8 * q^79 - 50 * q^80 - 8 * q^81 - 132 * q^84 + 12 * q^86 + 16 * q^89 - 116 * q^90 + 8 * q^91 - 8 * q^94 + 40 * q^95 + 104 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(595, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
595.2.ba.a	$595$	$2$	595.ba	35.j	$6$	$4$	$2$	$4.751$	\(\Q(\zeta_{12})\)	None		✓			595.2.ba.a	$4$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(-2+2\zeta_{12}^{2})q^{4}+(-\zeta_{12}+\cdots)q^{5}+\cdots\)
595.2.ba.b	$595$	$2$	595.ba	35.j	$6$	$124$	$62$	$4.751$		None		✓	✓		595.2.ba.b	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(595, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(595, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)