Space of modular forms of level 1856, weight 2, and Character 1856.e

• Label: 1856.2.e
• Level: $1856$
• Weight: $2$
• Character orbit: 1856.e
• Rep. character: $\chi_{1856}(1217,\cdot)$
• Character field: $\Q$
• Dimension: $58$
• Newform subspaces: $12$
• Sturm bound: $480$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1856 = 2^{6} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1856.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(480\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1856, [\chi])\).

	Total	New	Old
Modular forms	252	62	190
Cusp forms	228	58	170
Eisenstein series	24	4	20

Trace form

\( 58 q + 4 q^{5} - 58 q^{9} + 4 q^{13} + 54 q^{25} - 6 q^{29} + 8 q^{33} + 12 q^{45} + 42 q^{49} + 20 q^{53} + 8 q^{57} - 24 q^{65} + 82 q^{81} - 56 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1856, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1856.2.e.a	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	\(\Q(\sqrt{-7}) \)	None					116.2.c.a	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-q^{5}-2q^{7}-4q^{9}-\beta q^{11}+\cdots\)
1856.2.e.b	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	\(\Q(\sqrt{-1}) \)	None					58.2.b.a	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-q^{5}-2 q^{7}+2 q^{9}-5 i q^{11}+\cdots\)
1856.2.e.c	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	\(\Q(\sqrt{-7}) \)	None					116.2.c.a	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-q^{5}+2q^{7}-4q^{9}-\beta q^{11}+\cdots\)
1856.2.e.d	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	\(\Q(\sqrt{-1}) \)	None					58.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-q^{5}+2 q^{7}+2 q^{9}-5 i q^{11}+\cdots\)
1856.2.e.e	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					928.2.e.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2 q^{5}+3 q^{9}+6 q^{13}+4\beta q^{17}+\cdots\)
1856.2.e.f	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	\(\Q(\sqrt{-5}) \)	None					29.2.b.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+3q^{5}-2q^{7}-2q^{9}-\beta q^{11}+\cdots\)
1856.2.e.g	$1856$	$2$	1856.e	29.b	$2$	$2$	$2$	$14.820$	\(\Q(\sqrt{-5}) \)	None					29.2.b.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+3q^{5}+2q^{7}-2q^{9}-\beta q^{11}+\cdots\)
1856.2.e.h	$1856$	$2$	1856.e	29.b	$2$	$4$	$4$	$14.820$	\(\Q(i, \sqrt{5})\)	None					928.2.e.b	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}+2q^{9}+3\beta _{1}q^{11}+\cdots\)
1856.2.e.i	$1856$	$2$	1856.e	29.b	$2$	$8$	$8$	$14.820$	8.0.4589249536.2	None					232.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{4}q^{5}+(-1+\beta _{6})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1856.2.e.j	$1856$	$2$	1856.e	29.b	$2$	$8$	$8$	$14.820$	8.0.4589249536.2	None					232.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{4}q^{5}+(1-\beta _{6})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1856.2.e.k	$1856$	$2$	1856.e	29.b	$2$	$12$	$12$	$14.820$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	\(\Q(\sqrt{-29}) \)					928.2.e.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{7}q^{3}-\beta _{5}q^{5}+(-3+\beta _{1})q^{9}+\beta _{10}q^{11}+\cdots\)
1856.2.e.l	$1856$	$2$	1856.e	29.b	$2$	$12$	$12$	$14.820$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					928.2.e.c	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{5}q^{5}+\beta _{6}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1856, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1856, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(464, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(928, [\chi])\)\(^{\oplus 2}\)