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

• Label: 1950.2.z
• Level: $1950$
• Weight: $2$
• Character orbit: 1950.z
• Rep. character: $\chi_{1950}(1699,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $16$
• 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.z (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(840\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	888	80	808
Cusp forms	792	80	712
Eisenstein series	96	0	96

Trace form

80 * q + 40 * q^4 + 40 * q^9 + 8 * q^11 + 16 * q^14 - 40 * q^16 - 20 * q^19 + 8 * q^21 + 28 * q^26 - 4 * q^29 - 32 * q^31 - 56 * q^34 - 40 * q^36 + 4 * q^39 - 52 * q^41 + 16 * q^44 - 8 * q^46 + 36 * q^49 + 16 * q^51 + 8 * q^56 + 72 * q^59 + 20 * q^61 - 80 * q^64 - 48 * q^66 + 8 * q^69 + 80 * q^71 + 20 * q^74 + 20 * q^76 + 40 * q^79 - 40 * q^81 + 4 * q^84 + 48 * q^86 - 80 * q^89 - 36 * q^91 - 32 * q^94 + 16 * q^99

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.z.a	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		✓			1950.2.i.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.b	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None					78.2.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.c	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		✓			1950.2.i.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.d	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None					390.2.i.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.e	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None					390.2.i.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.f	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		✓			1950.2.i.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.g	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None					78.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.h	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None					390.2.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.i	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None					390.2.i.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.j	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None					390.2.i.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.k	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None					390.2.i.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.l	$1950$	$2$	1950.z	65.n	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		✓			1950.2.i.k	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
1950.2.z.m	$1950$	$2$	1950.z	65.n	$6$	$8$	$4$	$15.571$	8.0.1731891456.1	None		✓			1950.2.i.z	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{3}+\beta _{7})q^{2}+(-\beta _{3}-\beta _{7})q^{3}-\beta _{2}q^{4}+\cdots\)
1950.2.z.n	$1950$	$2$	1950.z	65.n	$6$	$8$	$4$	$15.571$	8.0.1731891456.1	None					390.2.i.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{7})q^{2}+(\beta _{3}+\beta _{7})q^{3}-\beta _{2}q^{4}+\cdots\)
1950.2.z.o	$1950$	$2$	1950.z	65.n	$6$	$8$	$4$	$15.571$	8.0.3317760000.2	None		✓			1950.2.i.ba	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
1950.2.z.p	$1950$	$2$	1950.z	65.n	$6$	$8$	$4$	$15.571$	8.0.3317760000.2	None		✓			1950.2.i.bc	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+\beta _{2}q^{6}+\cdots\)

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

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