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

• Label: 1950.2.f
• Level: $1950$
• Weight: $2$
• Character orbit: 1950.f
• Rep. character: $\chi_{1950}(649,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $16$
• Sturm bound: $840$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(840\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(19\), \(37\)

Dimensions

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

	Total	New	Old
Modular forms	444	44	400
Cusp forms	396	44	352
Eisenstein series	48	0	48

Trace form

44 * q + 44 * q^4 - 44 * q^9 + 16 * q^14 + 44 * q^16 + 32 * q^29 - 44 * q^36 + 12 * q^39 + 100 * q^49 - 24 * q^51 + 16 * q^56 + 96 * q^61 + 44 * q^64 + 32 * q^66 + 16 * q^69 + 8 * q^79 + 44 * q^81 + 48 * q^91 - 64 * 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.f.a	$1950$	$2$	1950.f	65.d	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.b.b	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+i q^{3}+q^{4}-i q^{6}-3 q^{7}+\cdots\)
1950.2.f.b	$1950$	$2$	1950.f	65.d	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.b.a	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-i q^{3}+q^{4}+i q^{6}-q^{8}+\cdots\)
1950.2.f.c	$1950$	$2$	1950.f	65.d	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.b.b	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+i q^{3}+q^{4}-i q^{6}-q^{8}+\cdots\)
1950.2.f.d	$1950$	$2$	1950.f	65.d	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					78.2.b.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+i q^{3}+q^{4}-i q^{6}+2 q^{7}+\cdots\)
1950.2.f.e	$1950$	$2$	1950.f	65.d	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.b.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-i q^{3}+q^{4}+i q^{6}+2 q^{7}+\cdots\)
1950.2.f.f	$1950$	$2$	1950.f	65.d	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.b.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+i q^{3}+q^{4}+i q^{6}-2 q^{7}+\cdots\)
1950.2.f.g	$1950$	$2$	1950.f	65.d	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					78.2.b.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+i q^{3}+q^{4}+i q^{6}-2 q^{7}+\cdots\)
1950.2.f.h	$1950$	$2$	1950.f	65.d	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.b.b	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-i q^{3}+q^{4}-i q^{6}+q^{8}+\cdots\)
1950.2.f.i	$1950$	$2$	1950.f	65.d	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.b.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-i q^{3}+q^{4}-i q^{6}+q^{8}+\cdots\)
1950.2.f.j	$1950$	$2$	1950.f	65.d	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.b.b	$2$	$0$	\(2\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-i q^{3}+q^{4}-i q^{6}+3 q^{7}+\cdots\)
1950.2.f.k	$1950$	$2$	1950.f	65.d	$2$	$4$	$4$	$15.571$	\(\Q(i, \sqrt{17})\)	None		✓			1950.2.b.i	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+(-3+\cdots)q^{7}+\cdots\)
1950.2.f.l	$1950$	$2$	1950.f	65.d	$2$	$4$	$4$	$15.571$	\(\Q(i, \sqrt{17})\)	None					390.2.b.d	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.2.f.m	$1950$	$2$	1950.f	65.d	$2$	$4$	$4$	$15.571$	\(\Q(i, \sqrt{13})\)	None					390.2.b.c	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1-\beta _{3})q^{7}+\cdots\)
1950.2.f.n	$1950$	$2$	1950.f	65.d	$2$	$4$	$4$	$15.571$	\(\Q(i, \sqrt{13})\)	None					390.2.b.c	$2$	$0$	\(4\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
1950.2.f.o	$1950$	$2$	1950.f	65.d	$2$	$4$	$4$	$15.571$	\(\Q(i, \sqrt{17})\)	None					390.2.b.d	$2$	$0$	\(4\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1950.2.f.p	$1950$	$2$	1950.f	65.d	$2$	$4$	$4$	$15.571$	\(\Q(i, \sqrt{17})\)	None		✓			1950.2.b.i	$2$	$0$	\(4\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}+(3-\beta _{3})q^{7}+\cdots\)

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

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