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

• Label: 575.2.i
• Level: $575$
• Weight: $2$
• Character orbit: 575.i
• Rep. character: $\chi_{575}(139,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $216$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.i (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	248	216	32
Cusp forms	232	216	16
Eisenstein series	16	0	16

Trace form

216 * q + 52 * q^4 + 2 * q^5 + 4 * q^6 - 30 * q^8 + 50 * q^9 - 2 * q^10 - 12 * q^14 - 10 * q^15 - 72 * q^16 + 36 * q^20 + 12 * q^21 + 20 * q^24 + 10 * q^25 - 56 * q^26 - 30 * q^27 + 60 * q^28 - 8 * q^29 - 14 * q^30 - 50 * q^33 - 26 * q^35 - 100 * q^36 - 70 * q^37 - 40 * q^38 - 36 * q^39 - 70 * q^40 + 2 * q^41 + 80 * q^42 + 42 * q^44 + 4 * q^46 - 30 * q^47 - 208 * q^49 - 82 * q^50 + 44 * q^51 + 30 * q^53 - 40 * q^54 + 6 * q^55 - 36 * q^56 - 50 * q^58 - 36 * q^59 - 6 * q^60 - 4 * q^61 + 60 * q^62 + 50 * q^63 + 58 * q^64 - 10 * q^65 - 42 * q^66 - 20 * q^67 - 8 * q^69 - 44 * q^70 + 14 * q^71 - 10 * q^72 - 40 * q^73 - 80 * q^74 + 24 * q^75 + 60 * q^76 - 60 * q^78 - 32 * q^79 - 32 * q^80 - 22 * q^81 - 30 * q^83 - 4 * q^84 + 48 * q^85 + 40 * q^86 + 50 * q^87 + 30 * q^88 + 48 * q^89 + 210 * q^90 + 12 * q^91 + 36 * q^94 + 36 * q^95 - 56 * q^96 + 140 * q^97 - 10 * 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.i.a	$575$	$2$	575.i	25.e	$10$	$216$	$54$	$4.591$		None		✓	✓	✓	575.2.i.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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