Space of modular forms of level 484, weight 2, and Character 484.e

• Label: 484.2.e
• Level: $484$
• Weight: $2$
• Character orbit: 484.e
• Rep. character: $\chi_{484}(9,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $36$
• Newform subspaces: $7$
• Sturm bound: $132$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.e (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(132\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(484, [\chi])\).

	Total	New	Old
Modular forms	336	36	300
Cusp forms	192	36	156
Eisenstein series	144	0	144

Trace form

36 * q - 4 * q^5 + 7 * q^7 - 3 * q^9 + q^13 - 2 * q^15 + q^17 - 7 * q^19 - 18 * q^21 - 12 * q^23 - 19 * q^25 - 6 * q^27 + 5 * q^29 + 4 * q^31 + 9 * q^35 + 10 * q^37 - 9 * q^39 + 5 * q^41 + 24 * q^45 + 7 * q^47 + 4 * q^49 + q^51 - 11 * q^53 - 17 * q^57 - 20 * q^59 + q^61 - 4 * q^63 + 2 * q^65 - 28 * q^67 - 7 * q^69 - 8 * q^71 - 19 * q^73 + 13 * q^75 - 3 * q^79 + 6 * q^81 + 31 * q^83 + 7 * q^85 + 50 * q^87 + 36 * q^89 + 71 * q^91 + 40 * q^93 + q^95 + 12 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(484, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
484.2.e.a	$484$	$2$	484.e	11.c	$5$	$4$	$1$	$3.865$	\(\Q(\zeta_{10})\)	None					44.2.a.a	$4$	$0$	\(0\)	\(-1\)	\(3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
484.2.e.b	$484$	$2$	484.e	11.c	$5$	$4$	$1$	$3.865$	\(\Q(\zeta_{10})\)	None					44.2.a.a	$4$	$0$	\(0\)	\(-1\)	\(3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
484.2.e.c	$484$	$2$	484.e	11.c	$5$	$4$	$1$	$3.865$	\(\Q(\zeta_{10})\)	None					44.2.e.a	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
484.2.e.d	$484$	$2$	484.e	11.c	$5$	$4$	$1$	$3.865$	\(\Q(\zeta_{10})\)	None					44.2.e.a	$2$	$0$	\(0\)	\(4\)	\(-2\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots\)
484.2.e.e	$484$	$2$	484.e	11.c	$5$	$4$	$1$	$3.865$	\(\Q(\zeta_{10})\)	None					44.2.e.a	$2$	$0$	\(0\)	\(4\)	\(-2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots\)
484.2.e.f	$484$	$2$	484.e	11.c	$5$	$8$	$2$	$3.865$	8.0.324000000.3	None		✓			484.2.a.e	$8$	$0$	\(0\)	\(-4\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+2\beta _{6}q^{3}+(-3-3\beta _{2}-3\beta _{4}-3\beta _{6}+\cdots)q^{5}+\cdots\)
484.2.e.g	$484$	$2$	484.e	11.c	$5$	$8$	$2$	$3.865$	8.0.\(\cdots\).3	\(\Q(\sqrt{-11}) \)		✓			484.2.a.d	$8$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)	$1$	$\mathrm{U}(1)[D_{5}]$	\(q-\beta _{1}q^{3}+(-2-2\beta _{2}-2\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(484, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(484, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 2}\)