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

• Label: 1950.2.i
• Level: $1950$
• Weight: $2$
• Character orbit: 1950.i
• Rep. character: $\chi_{1950}(451,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $92$
• Newform subspaces: $35$
• Sturm bound: $840$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 35 \)
Sturm bound:			\(840\)
Trace bound:			\(11\)
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	888	92	796
Cusp forms	792	92	700
Eisenstein series	96	0	96

Trace form

92 * q - 2 * q^2 - 46 * q^4 + 4 * q^8 - 46 * q^9 + 10 * q^13 - 16 * q^14 - 46 * q^16 + 2 * q^17 + 4 * q^18 - 12 * q^19 + 16 * q^21 + 8 * q^22 - 16 * q^23 + 26 * q^26 - 18 * q^29 - 48 * q^31 - 2 * q^32 + 4 * q^33 + 44 * q^34 - 46 * q^36 - 26 * q^37 + 8 * q^39 - 2 * q^41 + 4 * q^42 - 8 * q^43 - 8 * q^46 - 32 * q^47 - 66 * q^49 + 32 * q^51 + 4 * q^52 - 52 * q^53 + 8 * q^56 + 8 * q^57 + 14 * q^58 - 16 * q^59 - 6 * q^61 + 16 * q^62 + 92 * q^64 + 8 * q^66 + 16 * q^67 + 2 * q^68 - 12 * q^69 - 40 * q^71 - 2 * q^72 + 100 * q^73 - 2 * q^74 - 12 * q^76 - 16 * q^78 + 8 * q^79 - 46 * q^81 + 22 * q^82 - 48 * q^83 - 8 * q^84 - 48 * q^86 + 20 * q^87 + 8 * q^88 + 52 * q^89 - 20 * q^91 + 32 * q^92 + 8 * q^94 + 28 * q^97 - 10 * q^98

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.i.a	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.y.e	$2$	$1$	\(-1\)	\(-1\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.b	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					78.2.e.b	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.c	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None		✓			1950.2.i.c	$2$	$1$	\(-1\)	\(-1\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.d	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.i.f	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.e	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None		✓			1950.2.i.e	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.f	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.i.e	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.g	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.y.a	$2$	$1$	\(-1\)	\(-1\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.h	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None		✓			1950.2.i.h	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.i	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.i.d	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.j	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.y.f	$2$	$1$	\(-1\)	\(1\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.k	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None		✓			1950.2.i.k	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.l	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.y.d	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.m	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					78.2.e.a	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.n	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.i.c	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.o	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.i.b	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.p	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.y.d	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.q	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.y.f	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.r	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None		✓			1950.2.i.k	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.s	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.i.a	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.t	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.y.a	$2$	$1$	\(1\)	\(1\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.u	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None		✓			1950.2.i.h	$2$	$0$	\(1\)	\(1\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.v	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None		✓			1950.2.i.e	$2$	$0$	\(1\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.w	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None		✓			1950.2.i.c	$2$	$0$	\(1\)	\(1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.x	$1950$	$2$	1950.i	13.c	$3$	$2$	$1$	$15.571$	\(\Q(\sqrt{-3}) \)	None					390.2.y.e	$2$	$0$	\(1\)	\(1\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.y	$1950$	$2$	1950.i	13.c	$3$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None					390.2.y.b	$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2})q^{3}+\cdots\)
1950.2.i.z	$1950$	$2$	1950.i	13.c	$3$	$4$	$2$	$15.571$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		✓			1950.2.i.z	$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
1950.2.i.ba	$1950$	$2$	1950.i	13.c	$3$	$4$	$2$	$15.571$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		✓			1950.2.i.ba	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bb	$1950$	$2$	1950.i	13.c	$3$	$4$	$2$	$15.571$	\(\Q(\sqrt{-3}, \sqrt{11})\)	None					390.2.y.g	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bc	$1950$	$2$	1950.i	13.c	$3$	$4$	$2$	$15.571$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		✓			1950.2.i.bc	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bd	$1950$	$2$	1950.i	13.c	$3$	$4$	$2$	$15.571$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		✓			1950.2.i.bc	$2$	$0$	\(2\)	\(-2\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.be	$1950$	$2$	1950.i	13.c	$3$	$4$	$2$	$15.571$	\(\Q(\sqrt{-3}, \sqrt{11})\)	None					390.2.y.g	$2$	$0$	\(2\)	\(-2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bf	$1950$	$2$	1950.i	13.c	$3$	$4$	$2$	$15.571$	\(\Q(\sqrt{-3}, \sqrt{10})\)	None		✓			1950.2.i.ba	$2$	$0$	\(2\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bg	$1950$	$2$	1950.i	13.c	$3$	$4$	$2$	$15.571$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		✓			1950.2.i.z	$2$	$0$	\(2\)	\(2\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2})q^{2}+(1-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
1950.2.i.bh	$1950$	$2$	1950.i	13.c	$3$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None					390.2.y.b	$2$	$0$	\(2\)	\(2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1950.2.i.bi	$1950$	$2$	1950.i	13.c	$3$	$4$	$2$	$15.571$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None					390.2.i.g	$2$	$0$	\(2\)	\(2\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2})q^{2}+(1-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)

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

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