Space of modular forms of level 225, weight 4, and Character 225.q

• Label: 225.4.q
• Level: $225$
• Weight: $4$
• Character orbit: 225.q
• Rep. character: $\chi_{225}(16,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $704$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 225 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(225, [\chi])\).

	Total	New	Old
Modular forms	736	736	0
Cusp forms	704	704	0
Eisenstein series	32	32	0

Trace form

704 * q - 3 * q^2 - 2 * q^3 + 341 * q^4 - 20 * q^5 - 22 * q^6 - 8 * q^7 - 44 * q^8 - 38 * q^9 - 32 * q^10 + 85 * q^11 - 172 * q^12 - 3 * q^13 + 157 * q^14 + 423 * q^15 + 1325 * q^16 + 84 * q^17 - 492 * q^18 - 12 * q^19 - 137 * q^20 + 123 * q^21 - 35 * q^22 - 131 * q^23 - 66 * q^24 + 284 * q^25 + 2432 * q^26 + 1060 * q^27 + 340 * q^28 + 345 * q^29 - 78 * q^30 - 39 * q^31 - 372 * q^32 + 16 * q^33 + 13 * q^34 + 1784 * q^35 + 584 * q^36 - 156 * q^37 + 1795 * q^38 + 392 * q^39 + 169 * q^40 + 653 * q^41 - 1328 * q^42 - 8 * q^43 - 2060 * q^44 - 2375 * q^45 - 44 * q^46 + 1343 * q^47 - 235 * q^48 - 14904 * q^49 - 909 * q^50 - 236 * q^51 - 283 * q^52 + 1788 * q^53 - 49 * q^54 - 1274 * q^55 + 72 * q^56 + 3236 * q^57 + 469 * q^58 + 915 * q^59 + 291 * q^60 - 3 * q^61 + 6088 * q^62 + 2881 * q^63 - 9692 * q^64 + 120 * q^65 + 2638 * q^66 - 921 * q^67 + 2484 * q^68 - 2624 * q^69 - 1762 * q^70 + 24 * q^71 - 2272 * q^72 - 12 * q^73 - 3798 * q^74 - 2717 * q^75 + 88 * q^76 + 4759 * q^77 + 2068 * q^78 - 255 * q^79 - 15302 * q^80 - 158 * q^81 - 3808 * q^82 - 1027 * q^83 - 3353 * q^84 + 949 * q^85 + 4545 * q^86 + 4366 * q^87 + 2869 * q^88 - 524 * q^89 - 139 * q^90 + 2046 * q^91 + 299 * q^92 + 1622 * q^93 - 2519 * q^94 - 2177 * q^95 + 4733 * q^96 + 1941 * q^97 + 2486 * q^98 - 470 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(225, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
225.4.q.a	$225$	$4$	225.q	225.q	$15$	$704$	$88$	$13.275$		None		✓	✓	✓	225.4.q.a	$4$	$0$	\(-3\)	\(-2\)	\(-20\)	\(-8\)		$\mathrm{SU}(2)[C_{15}]$