Space of modular forms of level 1872, weight 2, and Character 1872.bf

• Label: 1872.2.bf
• Level: $1872$
• Weight: $2$
• Character orbit: 1872.bf
• Rep. character: $\chi_{1872}(1279,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $70$
• Newform subspaces: $15$
• Sturm bound: $672$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.bf (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(672\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1872, [\chi])\).

	Total	New	Old
Modular forms	720	70	650
Cusp forms	624	70	554
Eisenstein series	96	0	96

Trace form

\( 70 q + 6 q^{5} - 2 q^{37} + 18 q^{41} - 36 q^{53} + 12 q^{61} - 30 q^{65} - 2 q^{73} + 12 q^{85} - 6 q^{89} + 38 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1872, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1872.2.bf.a	$1872$	$2$	1872.bf	52.f	$4$	$2$	$1$	$14.948$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					208.2.k.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-i-1)q^{5}+(3 i+2)q^{13}+2 i q^{17}+\cdots\)
1872.2.bf.b	$1872$	$2$	1872.bf	52.f	$4$	$2$	$1$	$14.948$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			1872.2.bf.b	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-i-1)q^{5}+(-3 i+2)q^{13}+\cdots\)
1872.2.bf.c	$1872$	$2$	1872.bf	52.f	$4$	$2$	$1$	$14.948$	\(\Q(\sqrt{-1}) \)	None					624.2.bc.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2 i-2)q^{7}+(3 i+3)q^{11}+(2 i-3)q^{13}+\cdots\)
1872.2.bf.d	$1872$	$2$	1872.bf	52.f	$4$	$2$	$1$	$14.948$	\(\Q(\sqrt{-1}) \)	None					624.2.bc.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2 i+2)q^{7}+(-3 i-3)q^{11}+(2 i-3)q^{13}+\cdots\)
1872.2.bf.e	$1872$	$2$	1872.bf	52.f	$4$	$2$	$1$	$14.948$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			1872.2.bf.b	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(i+1)q^{5}+(-3 i+2)q^{13}-8 i q^{17}+\cdots\)
1872.2.bf.f	$1872$	$2$	1872.bf	52.f	$4$	$4$	$2$	$14.948$	\(\Q(\zeta_{12})\)	None		✓			1872.2.bf.f	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2\beta_1-2)q^{5}-\beta_{2} q^{7}+2\beta_{2} q^{11}+\cdots\)
1872.2.bf.g	$1872$	$2$	1872.bf	52.f	$4$	$4$	$2$	$14.948$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		✓			1872.2.bf.g	$4$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{3}$	$\mathrm{U}(1)[D_{4}]$	\(q+(\beta_{3}+2\beta_1-2)q^{7}+(-\beta_{3}-\beta_{2}+\beta_1)q^{13}+\cdots\)
1872.2.bf.h	$1872$	$2$	1872.bf	52.f	$4$	$4$	$2$	$14.948$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		✓			1872.2.bf.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{U}(1)[D_{4}]$	\(q+(-\beta_{3}-2\beta_1+2)q^{7}+(-\beta_{3}-\beta_{2}+\beta_1)q^{13}+\cdots\)
1872.2.bf.i	$1872$	$2$	1872.bf	52.f	$4$	$4$	$2$	$14.948$	\(\Q(i, \sqrt{17})\)	None					624.2.bc.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{1}+\beta _{3})q^{5}+(-2+2\beta _{1})q^{7}+\cdots\)
1872.2.bf.j	$1872$	$2$	1872.bf	52.f	$4$	$4$	$2$	$14.948$	\(\Q(i, \sqrt{17})\)	None					624.2.bc.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{1}+\beta _{3})q^{5}+(2-2\beta _{1})q^{7}+\beta _{3}q^{11}+\cdots\)
1872.2.bf.k	$1872$	$2$	1872.bf	52.f	$4$	$4$	$2$	$14.948$	\(\Q(\zeta_{12})\)	None		✓			1872.2.bf.f	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2\beta_1+2)q^{5}-\beta_{3} q^{7}-2\beta_{3} q^{11}+\cdots\)
1872.2.bf.l	$1872$	$2$	1872.bf	52.f	$4$	$8$	$4$	$14.948$	8.0.3317760000.5	None		✓			1872.2.bf.l	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{5}-\beta _{5}q^{7}+\beta _{7}q^{11}+(-3-2\beta _{3}+\cdots)q^{13}+\cdots\)
1872.2.bf.m	$1872$	$2$	1872.bf	52.f	$4$	$8$	$4$	$14.948$	8.0.56070144.2	None					624.2.bc.e	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-8\)	$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+(\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)
1872.2.bf.n	$1872$	$2$	1872.bf	52.f	$4$	$8$	$4$	$14.948$	8.0.56070144.2	None					624.2.bc.e	$2$	$0$	\(0\)	\(0\)	\(4\)	\(8\)	$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{5}+(1-\beta _{1})q^{7}+(-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots\)
1872.2.bf.o	$1872$	$2$	1872.bf	52.f	$4$	$12$	$6$	$14.948$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None			✓		208.2.k.b	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{5}+\beta _{10}q^{7}-\beta _{7}q^{11}+(-\beta _{5}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1872, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)