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

• Label: 484.2.g
• Level: $484$
• Weight: $2$
• Character orbit: 484.g
• Rep. character: $\chi_{484}(215,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $184$
• Newform subspaces: $11$
• Sturm bound: $132$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.g (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(132\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(5\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	312	248	64
Cusp forms	216	184	32
Eisenstein series	96	64	32

Trace form

184 * q + 5 * q^2 + q^4 + 6 * q^5 + 5 * q^6 + 5 * q^8 + 40 * q^9 - 18 * q^12 + 10 * q^13 - 12 * q^14 - 27 * q^16 + 10 * q^17 - 20 * q^18 - 12 * q^20 - 25 * q^24 - 16 * q^25 - 20 * q^26 - 20 * q^28 + 10 * q^29 - 18 * q^34 + 40 * q^36 - 18 * q^37 + 48 * q^38 + 40 * q^40 - 10 * q^41 - 14 * q^42 - 168 * q^45 + 30 * q^46 + 46 * q^48 + 4 * q^49 + 15 * q^50 + 10 * q^52 - 50 * q^53 - 52 * q^56 - 42 * q^58 - 104 * q^60 + 10 * q^61 - 70 * q^62 - 11 * q^64 - 60 * q^68 + 28 * q^69 - 45 * q^72 + 30 * q^73 - 40 * q^74 - 36 * q^78 + 88 * q^80 + 34 * q^81 + 69 * q^82 + 10 * q^84 + 50 * q^85 + 33 * q^86 - 28 * q^89 + 50 * q^90 - 36 * q^92 + 50 * q^93 + 30 * q^94 + 72 * 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.g.a	$484$	$2$	484.g	44.g	$10$	$8$	$2$	$3.865$	8.0.64000000.1	None		✓			484.2.c.c	$4$	$0$	\(0\)	\(-10\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{1}q^{2}+(-2+2\beta _{2}-\beta _{4})q^{3}+2\beta _{2}q^{4}+\cdots\)
484.2.g.b	$484$	$2$	484.g	44.g	$10$	$8$	$2$	$3.865$	8.0.64000000.1	None		✓			484.2.c.c	$4$	$0$	\(0\)	\(-10\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{1}q^{2}+(-2-2\beta _{4}+\beta _{6})q^{3}+2\beta _{2}q^{4}+\cdots\)
484.2.g.c	$484$	$2$	484.g	44.g	$10$	$8$	$2$	$3.865$	8.0.64000000.1	\(\Q(\sqrt{-1}) \)		✓			484.2.c.a	$16$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q+\beta _{1}q^{2}+2\beta _{2}q^{4}-4\beta _{4}q^{5}+2\beta _{3}q^{8}+\cdots\)
484.2.g.d	$484$	$2$	484.g	44.g	$10$	$8$	$2$	$3.865$	8.0.64000000.1	None		✓			484.2.c.c	$4$	$0$	\(0\)	\(10\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{5}q^{2}+(2-2\beta _{2}+\beta _{4})q^{3}-2q^{4}+\cdots\)
484.2.g.e	$484$	$2$	484.g	44.g	$10$	$8$	$2$	$3.865$	8.0.64000000.1	None		✓			484.2.c.c	$4$	$0$	\(0\)	\(10\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{1}q^{2}+(\beta _{2}-2\beta _{4}+2\beta _{6})q^{3}+2\beta _{2}q^{4}+\cdots\)
484.2.g.f	$484$	$2$	484.g	44.g	$10$	$16$	$4$	$3.865$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					44.2.g.a	$4$	$0$	\(-5\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{15}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
484.2.g.g	$484$	$2$	484.g	44.g	$10$	$16$	$4$	$3.865$	16.0.\(\cdots\).2	None					44.2.c.a	$16$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{5}q^{2}-\beta _{11}q^{3}+(-\beta _{2}-\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots\)
484.2.g.h	$484$	$2$	484.g	44.g	$10$	$16$	$4$	$3.865$	16.0.\(\cdots\).7	\(\Q(\sqrt{-1}) \)		✓			484.2.c.b	$16$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q+(-\beta _{1}+\beta _{3})q^{2}+2\beta _{4}q^{4}+(-2\beta _{8}+\cdots)q^{5}+\cdots\)
484.2.g.i	$484$	$2$	484.g	44.g	$10$	$16$	$4$	$3.865$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					44.2.g.a	$4$	$0$	\(5\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{2}q^{2}+(-1-\beta _{1}-\beta _{2}-\beta _{13}-\beta _{14}+\cdots)q^{3}+\cdots\)
484.2.g.j	$484$	$2$	484.g	44.g	$10$	$16$	$4$	$3.865$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					44.2.g.a	$4$	$0$	\(5\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{15}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
484.2.g.k	$484$	$2$	484.g	44.g	$10$	$64$	$16$	$3.865$		None		✓	✓		484.2.c.e	$16$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(484, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)