Space of modular forms of level 1950, weight 2, and Character 1950.b

• Label: 1950.2.b
• Level: $1950$
• Weight: $2$
• Character orbit: 1950.b
• Rep. character: $\chi_{1950}(1351,\cdot)$
• Character field: $\Q$
• Dimension: $42$
• Newform subspaces: $13$
• Sturm bound: $840$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(840\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1950, [\chi])\).

	Total	New	Old
Modular forms	444	42	402
Cusp forms	396	42	354
Eisenstein series	48	0	48

Trace form

42 * q + 2 * q^3 - 42 * q^4 + 42 * q^9 - 2 * q^12 + 2 * q^13 - 12 * q^14 + 42 * q^16 - 4 * q^17 - 8 * q^23 + 8 * q^26 + 2 * q^27 - 28 * q^29 - 42 * q^36 + 12 * q^38 - 18 * q^39 + 4 * q^42 - 24 * q^43 + 2 * q^48 - 58 * q^49 - 12 * q^51 - 2 * q^52 + 20 * q^53 + 12 * q^56 + 60 * q^61 + 28 * q^62 - 42 * q^64 + 4 * q^68 - 8 * q^69 + 56 * q^74 + 64 * q^77 - 12 * q^78 + 24 * q^79 + 42 * q^81 + 12 * q^82 + 12 * q^87 - 24 * q^91 + 8 * q^92 - 40 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(1950, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1950.2.b.a	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{3}-q^{4}+i q^{6}+2 i q^{7}+\cdots\)
1950.2.b.b	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.b.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{3}-q^{4}-i q^{6}+3 i q^{7}+\cdots\)
1950.2.b.c	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					78.2.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{3}-q^{4}+i q^{6}+2 i q^{7}+\cdots\)
1950.2.b.d	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.b.b	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{3}-q^{4}+i q^{6}+3 i q^{7}+\cdots\)
1950.2.b.e	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.b.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+q^{3}-q^{4}-i q^{6}+i q^{8}+\cdots\)
1950.2.b.f	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+q^{3}-q^{4}-i q^{6}+2 i q^{7}+\cdots\)
1950.2.b.g	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{3}-q^{4}+i q^{6}-i q^{8}+\cdots\)
1950.2.b.h	$1950$	$2$	1950.b	13.b	$2$	$4$	$4$	$15.571$	\(\Q(i, \sqrt{17})\)	None					390.2.b.d	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{3}-q^{4}+\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.2.b.i	$1950$	$2$	1950.b	13.b	$2$	$4$	$4$	$15.571$	\(\Q(i, \sqrt{17})\)	None		✓			1950.2.b.i	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{3}-q^{4}-\beta _{2}q^{6}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
1950.2.b.j	$1950$	$2$	1950.b	13.b	$2$	$4$	$4$	$15.571$	\(\Q(i, \sqrt{17})\)	None		✓			1950.2.b.i	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{6}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
1950.2.b.k	$1950$	$2$	1950.b	13.b	$2$	$4$	$4$	$15.571$	\(\Q(i, \sqrt{13})\)	None					390.2.b.c	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.2.b.l	$1950$	$2$	1950.b	13.b	$2$	$6$	$6$	$15.571$	6.0.350464.1	None					390.2.f.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-q^{3}-q^{4}-\beta _{4}q^{6}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
1950.2.b.m	$1950$	$2$	1950.b	13.b	$2$	$6$	$6$	$15.571$	6.0.350464.1	None					390.2.f.a	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+q^{3}-q^{4}+\beta _{4}q^{6}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)