Space of modular forms of level 950, weight 2, and Character 950.b

• Label: 950.2.b
• Level: $950$
• Weight: $2$
• Character orbit: 950.b
• Rep. character: $\chi_{950}(799,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $8$
• Sturm bound: $300$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(300\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(950, [\chi])\).

	Total	New	Old
Modular forms	162	26	136
Cusp forms	138	26	112
Eisenstein series	24	0	24

Trace form

26 * q - 26 * q^4 + 4 * q^6 - 38 * q^9 + 8 * q^11 - 8 * q^14 + 26 * q^16 + 2 * q^19 + 32 * q^21 - 4 * q^24 - 24 * q^26 - 28 * q^29 + 4 * q^34 + 38 * q^36 - 8 * q^39 - 12 * q^41 - 8 * q^44 + 40 * q^46 - 62 * q^49 + 40 * q^51 - 16 * q^54 + 8 * q^56 - 24 * q^59 + 36 * q^61 - 26 * q^64 + 56 * q^69 + 8 * q^71 + 48 * q^74 - 2 * q^76 - 48 * q^79 + 42 * q^81 - 32 * q^84 + 52 * q^89 - 24 * q^91 - 56 * q^94 + 4 * q^96 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(950, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
950.2.b.a	$950$	$2$	950.b	5.b	$2$	$2$	$2$	$7.586$	\(\Q(\sqrt{-1}) \)	None					190.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+3 i q^{3}-q^{4}-3 q^{6}-5 i q^{7}+\cdots\)
950.2.b.b	$950$	$2$	950.b	5.b	$2$	$2$	$2$	$7.586$	\(\Q(\sqrt{-1}) \)	None					38.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
950.2.b.c	$950$	$2$	950.b	5.b	$2$	$2$	$2$	$7.586$	\(\Q(\sqrt{-1}) \)	None					38.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+3 i q^{7}+\cdots\)
950.2.b.d	$950$	$2$	950.b	5.b	$2$	$2$	$2$	$7.586$	\(\Q(\sqrt{-1}) \)	None					190.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}-i q^{7}+\cdots\)
950.2.b.e	$950$	$2$	950.b	5.b	$2$	$2$	$2$	$7.586$	\(\Q(\sqrt{-1}) \)	None					190.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+i q^{7}+\cdots\)
950.2.b.f	$950$	$2$	950.b	5.b	$2$	$4$	$4$	$7.586$	\(\Q(i, \sqrt{17})\)	None					190.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
950.2.b.g	$950$	$2$	950.b	5.b	$2$	$6$	$6$	$7.586$	6.0.4227136.2	None		✓			950.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4})q^{3}-q^{4}+\cdots\)
950.2.b.h	$950$	$2$	950.b	5.b	$2$	$6$	$6$	$7.586$	6.0.63107136.1	None		✓			950.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(950, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)