Space of modular forms of level 75, weight 2, and Character 75.i

• Label: 75.2.i
• Level: $75$
• Weight: $2$
• Character orbit: 75.i
• Rep. character: $\chi_{75}(4,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.i (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(75, [\chi])\).

	Total	New	Old
Modular forms	48	16	32
Cusp forms	32	16	16
Eisenstein series	16	0	16

Trace form

16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 + 10 * q^17 - 2 * q^19 + 20 * q^20 + 4 * q^21 - 30 * q^22 - 20 * q^23 + 24 * q^24 - 10 * q^25 + 12 * q^26 + 30 * q^28 + 16 * q^29 - 20 * q^30 + 6 * q^31 + 10 * q^33 - 36 * q^34 + 10 * q^35 - 2 * q^36 - 10 * q^37 + 30 * q^38 - 8 * q^39 + 10 * q^40 - 14 * q^41 - 10 * q^42 + 26 * q^44 + 16 * q^46 + 40 * q^47 + 20 * q^50 - 32 * q^51 + 40 * q^52 + 10 * q^53 - 2 * q^54 + 10 * q^55 + 10 * q^58 + 12 * q^59 - 30 * q^60 - 10 * q^62 - 10 * q^63 + 8 * q^64 - 70 * q^65 + 16 * q^66 - 40 * q^67 - 12 * q^69 + 30 * q^70 - 8 * q^71 - 30 * q^72 - 20 * q^73 - 52 * q^74 - 32 * q^76 - 40 * q^77 - 20 * q^79 - 4 * q^81 + 10 * q^83 + 12 * q^84 - 20 * q^85 - 36 * q^86 + 40 * q^87 - 40 * q^88 + 18 * q^89 + 30 * q^90 + 26 * q^91 + 10 * q^92 - 38 * q^94 - 40 * q^95 - 26 * q^96 + 40 * q^97 + 60 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(75, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
75.2.i.a	$75$	$2$	75.i	25.e	$10$	$16$	$4$	$0.599$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	75.2.i.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1-\beta _{2}-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{8}+\cdots)q^{2}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(75, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(75, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)