Space of modular forms of level 1840, weight 2, and Character 1840.e

• Label: 1840.2.e
• Level: $1840$
• Weight: $2$
• Character orbit: 1840.e
• Rep. character: $\chi_{1840}(369,\cdot)$
• Character field: $\Q$
• Dimension: $66$
• Newform subspaces: $8$
• Sturm bound: $576$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1840.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(576\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1840, [\chi])\).

	Total	New	Old
Modular forms	300	66	234
Cusp forms	276	66	210
Eisenstein series	24	0	24

Trace form

66 * q + 2 * q^5 - 66 * q^9 + 10 * q^25 - 4 * q^29 + 12 * q^31 - 12 * q^35 - 40 * q^39 - 4 * q^41 - 10 * q^45 - 82 * q^49 + 24 * q^51 + 16 * q^55 + 52 * q^59 + 20 * q^61 - 8 * q^65 + 36 * q^71 - 48 * q^75 - 48 * q^79 + 66 * q^81 - 8 * q^85 + 20 * q^89 + 32 * q^91 - 48 * q^95 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1840, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1840.2.e.a	$1840$	$2$	1840.e	5.b	$2$	$2$	$2$	$14.692$	\(\Q(\sqrt{-1}) \)	None					920.2.e.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}+(i+2)q^{5}-3 i q^{7}-q^{9}+\cdots\)
1840.2.e.b	$1840$	$2$	1840.e	5.b	$2$	$2$	$2$	$14.692$	\(\Q(\sqrt{-1}) \)	None					115.2.b.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}+(i+2)q^{5}-i q^{7}-q^{9}+\cdots\)
1840.2.e.c	$1840$	$2$	1840.e	5.b	$2$	$4$	$4$	$14.692$	\(\Q(i, \sqrt{5})\)	None					230.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(1+2\beta _{2})q^{5}+(3\beta _{1}+3\beta _{3})q^{7}+\cdots\)
1840.2.e.d	$1840$	$2$	1840.e	5.b	$2$	$8$	$8$	$14.692$	8.0.527896576.2	None					115.2.b.b	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2}+\beta _{4})q^{3}+(-1-\beta _{6}+\cdots)q^{5}+\cdots\)
1840.2.e.e	$1840$	$2$	1840.e	5.b	$2$	$8$	$8$	$14.692$	8.0.\(\cdots\).3	None					230.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{2}-\beta _{5})q^{3}+(\beta _{3}+\beta _{6})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1840.2.e.f	$1840$	$2$	1840.e	5.b	$2$	$12$	$12$	$14.692$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					460.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{5}+\beta _{6})q^{3}-\beta _{8}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)
1840.2.e.g	$1840$	$2$	1840.e	5.b	$2$	$14$	$14$	$14.692$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					920.2.e.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{3}-\beta _{5}q^{5}+(\beta _{7}-\beta _{13})q^{7}+(1+\cdots)q^{9}+\cdots\)
1840.2.e.h	$1840$	$2$	1840.e	5.b	$2$	$16$	$16$	$14.692$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		920.2.e.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-\beta _{10}q^{5}+(-\beta _{2}+\beta _{13})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)