Space of modular forms of level 75, weight 2, and Character 75.b

• Label: 75.2.b
• Level: $75$
• Weight: $2$
• Character orbit: 75.b
• Rep. character: $\chi_{75}(49,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $20$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(20\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(75, [\chi])\).

	Total	New	Old
Modular forms	16	4	12
Cusp forms	4	4	0
Eisenstein series	12	0	12

Trace form

4 * q - 2 * q^4 - 2 * q^6 - 4 * q^9 - 4 * q^11 + 12 * q^14 - 10 * q^16 + 2 * q^19 + 6 * q^21 + 6 * q^24 + 8 * q^26 - 16 * q^29 - 6 * q^31 - 4 * q^34 + 2 * q^36 - 2 * q^39 + 4 * q^41 - 16 * q^44 + 24 * q^46 + 10 * q^49 - 8 * q^51 + 2 * q^54 + 28 * q^59 + 10 * q^61 + 2 * q^64 - 16 * q^66 + 12 * q^69 - 32 * q^71 - 28 * q^74 - 28 * q^76 + 4 * q^81 - 12 * q^84 - 4 * q^86 + 12 * q^89 - 6 * q^91 + 8 * q^94 + 26 * q^96 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(75, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
75.2.b.a	$75$	$2$	75.b	5.b	$2$	$2$	$2$	$0.599$	\(\Q(\sqrt{-1}) \)	None		✓			75.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+i q^{3}-2 q^{4}-2 q^{6}-3 i q^{7}+\cdots\)
75.2.b.b	$75$	$2$	75.b	5.b	$2$	$2$	$2$	$0.599$	\(\Q(\sqrt{-1}) \)	None					15.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+q^{6}+3 i q^{8}+\cdots\)