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

• Label: 1950.2.e
• Level: $1950$
• Weight: $2$
• Character orbit: 1950.e
• Rep. character: $\chi_{1950}(1249,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $16$
• Sturm bound: $840$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(840\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\), \(31\)

Dimensions

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

	Total	New	Old
Modular forms	444	36	408
Cusp forms	396	36	360
Eisenstein series	48	0	48

Trace form

36 * q - 36 * q^4 + 4 * q^6 - 36 * q^9 + 16 * q^11 + 36 * q^16 - 8 * q^19 + 8 * q^21 - 4 * q^24 + 16 * q^29 - 24 * q^31 - 16 * q^34 + 36 * q^36 - 32 * q^41 - 16 * q^44 + 32 * q^46 - 12 * q^49 - 16 * q^51 - 4 * q^54 + 32 * q^61 - 36 * q^64 + 16 * q^69 - 32 * q^71 + 32 * q^74 + 8 * q^76 - 8 * q^79 + 36 * q^81 - 8 * q^84 - 64 * q^86 - 16 * q^89 - 8 * q^91 + 32 * q^94 + 4 * q^96 - 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.e.a	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
1950.2.e.b	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
1950.2.e.c	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+4 i q^{7}+\cdots\)
1950.2.e.d	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+2 i q^{7}+\cdots\)
1950.2.e.e	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+4 i q^{7}+\cdots\)
1950.2.e.f	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+2 i q^{7}+\cdots\)
1950.2.e.g	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}-i q^{8}+\cdots\)
1950.2.e.h	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}-i q^{8}+\cdots\)
1950.2.e.i	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					78.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+4 i q^{7}+\cdots\)
1950.2.e.j	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}+3 i q^{7}+\cdots\)
1950.2.e.k	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}+2 i q^{7}+\cdots\)
1950.2.e.l	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}-i q^{8}+\cdots\)
1950.2.e.m	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None					390.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}+2 i q^{7}+\cdots\)
1950.2.e.n	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	\(\Q(\sqrt{-1}) \)	None		✓			1950.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+4 i q^{7}+\cdots\)
1950.2.e.o	$1950$	$2$	1950.e	5.b	$2$	$4$	$4$	$15.571$	\(\Q(\zeta_{8})\)	None					390.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}+\beta_1 q^{3}-q^{4}+q^{6}+\beta_{2} q^{7}+\cdots\)
1950.2.e.p	$1950$	$2$	1950.e	5.b	$2$	$4$	$4$	$15.571$	\(\Q(i, \sqrt{41})\)	None		✓			1950.2.a.bc	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+q^{6}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)