Space of modular forms of level 575, weight 2, and Character 575.g

• Label: 575.2.g
• Level: $575$
• Weight: $2$
• Character orbit: 575.g
• Rep. character: $\chi_{575}(116,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $224$
• Newform subspaces: $3$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(575, [\chi])\).

	Total	New	Old
Modular forms	248	224	24
Cusp forms	232	224	8
Eisenstein series	16	0	16

Trace form

224 * q - 2 * q^2 - 58 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7 + 12 * q^8 - 60 * q^9 - 24 * q^10 - 16 * q^12 - 16 * q^13 - 12 * q^14 - 10 * q^15 - 38 * q^16 - 28 * q^17 + 12 * q^18 + 20 * q^20 - 12 * q^21 - 24 * q^22 + 20 * q^24 - 24 * q^25 + 36 * q^26 - 6 * q^27 + 24 * q^28 - 28 * q^29 - 66 * q^30 - 8 * q^32 - 18 * q^33 + 30 * q^34 - 46 * q^35 - 10 * q^36 + 36 * q^37 + 8 * q^38 - 36 * q^39 - 22 * q^41 + 16 * q^42 - 32 * q^43 + 42 * q^44 + 66 * q^45 - 4 * q^46 + 6 * q^47 - 60 * q^48 + 232 * q^49 - 44 * q^51 - 60 * q^52 + 4 * q^53 - 40 * q^54 - 10 * q^55 + 36 * q^56 + 80 * q^57 + 54 * q^58 - 36 * q^59 + 106 * q^60 - 16 * q^61 - 32 * q^62 - 50 * q^63 - 52 * q^64 + 56 * q^65 + 42 * q^66 + 44 * q^67 + 84 * q^68 - 8 * q^69 - 24 * q^70 - 14 * q^71 + 44 * q^72 - 52 * q^73 - 100 * q^74 - 76 * q^75 - 60 * q^76 + 4 * q^77 - 104 * q^78 - 32 * q^79 + 158 * q^80 - 88 * q^81 - 40 * q^82 + 6 * q^83 - 4 * q^84 + 86 * q^85 - 40 * q^86 - 62 * q^87 + 158 * q^88 + 78 * q^89 - 12 * q^91 - 56 * q^93 + 36 * q^94 - 100 * q^95 + 56 * q^96 + 20 * q^97 - 60 * q^98 - 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(575, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
575.2.g.a	$575$	$2$	575.g	25.d	$5$	$4$	$1$	$4.591$	\(\Q(\zeta_{10})\)	None		✓			575.2.g.a	$2$	$1$	\(1\)	\(-5\)	\(-5\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
575.2.g.b	$575$	$2$	575.g	25.d	$5$	$108$	$27$	$4.591$		None		✓			575.2.g.b	$2$	$0$	\(-4\)	\(1\)	\(3\)	\(24\)		$\mathrm{SU}(2)[C_{5}]$
575.2.g.c	$575$	$2$	575.g	25.d	$5$	$112$	$28$	$4.591$		None		✓	✓		575.2.g.c	$2$	$0$	\(1\)	\(4\)	\(-2\)	\(-36\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(575, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)