Space of modular forms of level 300, weight 2, and Character 300.o

• Label: 300.2.o
• Level: $300$
• Weight: $2$
• Character orbit: 300.o
• Rep. character: $\chi_{300}(109,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(300, [\chi])\).

	Total	New	Old
Modular forms	264	24	240
Cusp forms	216	24	192
Eisenstein series	48	0	48

Trace form

24 * q - 2 * q^5 + 6 * q^9 - 6 * q^11 + 4 * q^15 + 10 * q^17 + 10 * q^19 - 4 * q^21 + 40 * q^23 - 4 * q^25 + 4 * q^29 + 6 * q^31 + 10 * q^33 - 6 * q^35 - 10 * q^41 + 2 * q^45 - 40 * q^47 - 56 * q^49 + 16 * q^51 - 60 * q^53 - 62 * q^55 - 36 * q^59 - 12 * q^61 - 10 * q^63 + 20 * q^67 + 4 * q^69 + 40 * q^71 + 60 * q^73 + 8 * q^75 - 40 * q^77 + 8 * q^79 - 6 * q^81 - 50 * q^83 + 34 * q^85 - 20 * q^87 - 30 * q^91 - 60 * q^95 - 40 * q^97 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(300, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
300.2.o.a	$300$	$2$	300.o	25.e	$10$	$24$	$6$	$2.396$		None		✓	✓	✓	300.2.o.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(300, [\chi])\) into lower level spaces

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