Space of modular forms of level 95, weight 3, and Character 95.d

• Label: 95.3.d
• Level: $95$
• Weight: $3$
• Character orbit: 95.d
• Rep. character: $\chi_{95}(94,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $4$
• Sturm bound: $30$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	95.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(30\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(95, [\chi])\).

	Total	New	Old
Modular forms	22	22	0
Cusp forms	18	18	0
Eisenstein series	4	4	0

Trace form

18 * q + 32 * q^4 - q^5 - 8 * q^6 + 38 * q^9 - 22 * q^11 + 72 * q^16 + 10 * q^19 + 60 * q^20 - 256 * q^24 + 55 * q^25 - 176 * q^26 - 264 * q^30 + 41 * q^35 + 32 * q^36 + 184 * q^39 - 144 * q^44 + 33 * q^45 + 164 * q^49 - 13 * q^55 - 30 * q^61 + 392 * q^64 + 168 * q^66 + 384 * q^74 - 24 * q^76 + 256 * q^80 + 594 * q^81 + 195 * q^85 - 597 * q^95 - 1312 * q^96 - 1178 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(95, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
95.3.d.a	$95$	$3$	95.d	95.d	$2$	$2$	$2$	$2.589$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)		✓			95.3.d.a	$4$	$0$	\(0\)	\(0\)	\(-9\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-4q^{4}+(-4-\beta )q^{5}+(-3+6\beta )q^{7}+\cdots\)
95.3.d.b	$95$	$3$	95.d	95.d	$2$	$4$	$4$	$2.589$	\(\Q(\sqrt{8 + \sqrt{19}})\)	\(\Q(\sqrt{-95}) \)	✓	✓			95.3.d.b	$4$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(4+\beta _{3})q^{4}+\cdots\)
95.3.d.c	$95$	$3$	95.d	95.d	$2$	$4$	$4$	$2.589$	\(\Q(\sqrt{18 +2 \sqrt{5}})\)	\(\Q(\sqrt{-95}) \)	✓	✓			95.3.d.c	$4$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(4+3\beta _{3})q^{4}+\cdots\)
95.3.d.d	$95$	$3$	95.d	95.d	$2$	$8$	$8$	$2.589$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓		95.3.d.d	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+2\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots\)