Space of modular forms of level 33, weight 4, and Character 33.e

• Label: 33.4.e
• Level: $33$
• Weight: $4$
• Character orbit: 33.e
• Rep. character: $\chi_{33}(4,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(16\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(33, [\chi])\).

	Total	New	Old
Modular forms	56	24	32
Cusp forms	40	24	16
Eisenstein series	16	0	16

Trace form

24 * q + 4 * q^2 - 44 * q^4 + 16 * q^5 + 12 * q^6 + 52 * q^7 - 116 * q^8 - 54 * q^9 - 112 * q^10 - 100 * q^11 + 24 * q^12 + 76 * q^13 + 418 * q^14 + 150 * q^15 + 368 * q^16 + 148 * q^17 - 54 * q^18 - 8 * q^19 - 354 * q^20 - 336 * q^21 - 674 * q^22 - 624 * q^23 - 126 * q^24 - 86 * q^25 - 478 * q^26 + 42 * q^28 + 820 * q^29 + 684 * q^30 + 230 * q^31 + 1416 * q^32 - 66 * q^33 + 1488 * q^34 + 240 * q^35 - 396 * q^36 + 108 * q^37 + 46 * q^38 + 336 * q^39 - 1282 * q^40 - 1460 * q^41 + 168 * q^42 - 360 * q^43 - 154 * q^44 + 144 * q^45 - 1766 * q^46 - 536 * q^47 + 336 * q^48 - 1794 * q^49 - 1578 * q^50 - 216 * q^51 + 1606 * q^52 + 1016 * q^53 - 432 * q^54 + 2940 * q^55 + 132 * q^56 - 1044 * q^57 + 50 * q^58 - 1060 * q^59 - 972 * q^60 + 1680 * q^61 - 272 * q^62 + 468 * q^63 - 208 * q^64 + 4240 * q^65 + 1296 * q^66 - 896 * q^67 + 3880 * q^68 + 540 * q^69 - 584 * q^70 + 1104 * q^71 + 1206 * q^72 + 866 * q^73 - 306 * q^74 + 1920 * q^75 - 6048 * q^76 - 724 * q^77 - 240 * q^78 + 84 * q^79 - 4078 * q^80 - 486 * q^81 + 1626 * q^82 - 7984 * q^83 - 1620 * q^84 - 2340 * q^85 - 5672 * q^86 - 6588 * q^87 + 1728 * q^88 - 3320 * q^89 - 828 * q^90 + 2500 * q^91 + 6782 * q^92 - 1788 * q^93 + 4406 * q^94 + 3768 * q^95 + 2334 * q^96 + 4008 * q^97 + 13640 * q^98 + 900 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(33, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
33.4.e.a	$33$	$4$	33.e	11.c	$5$	$4$	$1$	$1.947$	\(\Q(\zeta_{10})\)	None		✓			33.4.e.a	$2$	$0$	\(10\)	\(-3\)	\(-21\)	\(37\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(4-2\zeta_{10}+4\zeta_{10}^{2})q^{2}-3\zeta_{10}^{3}q^{3}+\cdots\)
33.4.e.b	$33$	$4$	33.e	11.c	$5$	$8$	$2$	$1.947$	8.0.682515625.5	None		✓			33.4.e.b	$2$	$0$	\(-6\)	\(-6\)	\(9\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}-2\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+\cdots\)
33.4.e.c	$33$	$4$	33.e	11.c	$5$	$12$	$3$	$1.947$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		33.4.e.c	$2$	$0$	\(0\)	\(9\)	\(28\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\beta _{3}-\beta _{5}-\beta _{6}-\beta _{7})q^{2}-3\beta _{6}q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(33, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(33, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)