Space of modular forms of level 880, weight 2, and Character 880.cd

• Label: 880.2.cd
• Level: $880$
• Weight: $2$
• Character orbit: 880.cd
• Rep. character: $\chi_{880}(49,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $136$
• Newform subspaces: $5$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cd (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(880, [\chi])\).

	Total	New	Old
Modular forms	624	152	472
Cusp forms	528	136	392
Eisenstein series	96	16	80

Trace form

136 * q - 3 * q^5 + 24 * q^9 + 8 * q^11 + 15 * q^15 + 18 * q^19 - 28 * q^21 + 5 * q^25 - 6 * q^29 + 6 * q^31 + 31 * q^35 + 38 * q^39 + 6 * q^41 - 4 * q^45 - 12 * q^49 - 42 * q^51 + 43 * q^55 + 14 * q^59 - 6 * q^61 - 18 * q^65 + 12 * q^69 + 22 * q^71 - 9 * q^75 - 14 * q^79 - 36 * q^81 - 37 * q^85 - 8 * q^89 + 26 * q^91 - 37 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(880, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
880.2.cd.a	$880$	$2$	880.cd	55.j	$10$	$8$	$2$	$7.027$	\(\Q(\zeta_{20})\)	None					110.2.j.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(2\zeta_{20}+2\zeta_{20}^{5})q^{3}+(-\zeta_{20}+\zeta_{20}^{3}+\cdots)q^{5}+\cdots\)
880.2.cd.b	$880$	$2$	880.cd	55.j	$10$	$16$	$4$	$7.027$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					110.2.j.b	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{6}+\beta _{10}+\beta _{12})q^{3}-\beta _{8}q^{5}+(1+\cdots)q^{7}+\cdots\)
880.2.cd.c	$880$	$2$	880.cd	55.j	$10$	$16$	$4$	$7.027$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					55.2.j.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-\beta _{5}-\beta _{13}+\beta _{15})q^{3}+(-\beta _{3}+\beta _{6}+\cdots)q^{5}+\cdots\)
880.2.cd.d	$880$	$2$	880.cd	55.j	$10$	$24$	$6$	$7.027$		None					220.2.t.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
880.2.cd.e	$880$	$2$	880.cd	55.j	$10$	$72$	$18$	$7.027$		None			✓		440.2.bn.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(880, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)