Space of modular forms of level 75, weight 4, and Character 75.i

• Label: 75.4.i
• Level: $75$
• Weight: $4$
• Character orbit: 75.i
• Rep. character: $\chi_{75}(4,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $64$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(40\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(75, [\chi])\).

	Total	New	Old
Modular forms	128	64	64
Cusp forms	112	64	48
Eisenstein series	16	0	16

Trace form

64 * q + 72 * q^4 - 6 * q^5 - 12 * q^6 + 210 * q^8 + 144 * q^9 - 14 * q^10 - 84 * q^11 - 132 * q^14 - 54 * q^15 - 460 * q^16 + 320 * q^17 + 188 * q^19 - 404 * q^20 - 84 * q^21 + 290 * q^22 - 160 * q^23 - 576 * q^24 - 496 * q^25 + 348 * q^26 - 360 * q^28 - 604 * q^29 + 564 * q^30 - 786 * q^31 + 480 * q^33 + 584 * q^34 + 1160 * q^35 - 648 * q^36 + 1030 * q^37 + 2490 * q^38 + 312 * q^39 + 3072 * q^40 + 884 * q^41 - 1020 * q^42 - 1694 * q^44 + 54 * q^45 - 1436 * q^46 - 1720 * q^47 - 5220 * q^49 - 3644 * q^50 + 1632 * q^51 - 3720 * q^52 - 5170 * q^53 + 108 * q^54 + 1484 * q^55 - 2700 * q^56 + 5030 * q^58 + 1392 * q^59 - 2646 * q^60 - 240 * q^61 + 8830 * q^62 - 180 * q^63 + 6618 * q^64 + 4582 * q^65 + 744 * q^66 - 4980 * q^67 - 72 * q^69 - 3180 * q^70 - 1432 * q^71 + 1890 * q^72 + 840 * q^73 + 2908 * q^74 + 576 * q^75 + 8832 * q^76 + 1120 * q^77 - 320 * q^79 - 444 * q^80 - 1296 * q^81 + 9380 * q^83 + 4392 * q^84 - 602 * q^85 + 3996 * q^86 + 2280 * q^87 + 2030 * q^88 - 1242 * q^89 - 144 * q^90 + 1484 * q^91 - 11230 * q^92 - 4018 * q^94 - 9884 * q^95 - 4344 * q^96 - 3870 * q^97 - 7020 * q^98 - 504 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(75, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
75.4.i.a	$75$	$4$	75.i	25.e	$10$	$64$	$16$	$4.425$		None		✓	✓	✓	75.4.i.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{4}^{\mathrm{old}}(75, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(75, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)