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

• Label: 225.4.m
• Level: $225$
• Weight: $4$
• Character orbit: 225.m
• Rep. character: $\chi_{225}(19,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $144$
• Newform subspaces: $3$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.m (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	376	152	224
Cusp forms	344	144	200
Eisenstein series	32	8	24

Trace form

144 * q + 5 * q^2 + 133 * q^4 - 9 * q^5 - 100 * q^8 + 31 * q^10 + q^11 - 5 * q^13 + 101 * q^14 - 607 * q^16 - 155 * q^17 - 43 * q^19 + 9 * q^20 - 690 * q^22 + 85 * q^23 + 109 * q^25 + 474 * q^26 - 45 * q^28 + 479 * q^29 - 195 * q^31 - 95 * q^34 - 1350 * q^35 - 520 * q^37 - 2745 * q^38 + 542 * q^40 - 767 * q^41 + 1178 * q^44 - 903 * q^46 + 1815 * q^47 - 5764 * q^49 + 1479 * q^50 + 2040 * q^52 + 2590 * q^53 + 549 * q^55 - 460 * q^56 + 2610 * q^58 + 513 * q^59 + 765 * q^61 - 1950 * q^62 + 1908 * q^64 - 1412 * q^65 + 3475 * q^67 - 1650 * q^70 - 1041 * q^71 + 835 * q^73 - 6504 * q^74 - 3736 * q^76 - 4990 * q^77 - 689 * q^79 + 4114 * q^80 - 4755 * q^83 - 962 * q^85 - 99 * q^86 + 870 * q^88 + 3652 * q^89 + 2282 * q^91 + 7140 * q^92 + 1693 * q^94 + 6339 * q^95 - 7835 * q^97 + 1840 * q^98

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.m.a	$225$	$4$	225.m	25.e	$10$	$24$	$6$	$13.275$		None					25.4.e.a	$2$	$0$	\(5\)	\(0\)	\(-15\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
225.4.m.b	$225$	$4$	225.m	25.e	$10$	$56$	$14$	$13.275$		None		✓			225.4.m.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
225.4.m.c	$225$	$4$	225.m	25.e	$10$	$64$	$16$	$13.275$		None			✓		75.4.i.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{4}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(225, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)