Space of modular forms of level 300, weight 4, and Character 300.o

• Label: 300.4.o
• Level: $300$
• Weight: $4$
• Character orbit: 300.o
• Rep. character: $\chi_{300}(109,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	300.o (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(300, [\chi])\).

	Total	New	Old
Modular forms	744	56	688
Cusp forms	696	56	640
Eisenstein series	48	0	48

Trace form

56 * q + 20 * q^5 + 126 * q^9 - 84 * q^11 + 30 * q^15 + 320 * q^17 - 40 * q^19 + 84 * q^21 - 580 * q^23 - 390 * q^25 + 224 * q^29 + 414 * q^31 + 480 * q^33 + 1080 * q^35 - 700 * q^37 + 400 * q^41 - 180 * q^45 + 1720 * q^47 - 876 * q^49 - 816 * q^51 + 1020 * q^53 + 1860 * q^55 - 576 * q^59 + 2572 * q^61 - 180 * q^63 - 960 * q^65 - 360 * q^67 - 1176 * q^69 - 40 * q^71 - 3720 * q^73 - 600 * q^75 + 1120 * q^77 - 1732 * q^79 - 1134 * q^81 - 1000 * q^83 + 2600 * q^85 - 1140 * q^87 + 3240 * q^89 + 3380 * q^91 + 1680 * q^95 + 3570 * q^97 - 504 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(300, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
300.4.o.a	$300$	$4$	300.o	25.e	$10$	$56$	$14$	$17.701$		None		✓	✓	✓	300.4.o.a	$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{4}^{\mathrm{old}}(300, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(300, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)