Space of modular forms of level 52, weight 10, and Character 52.e

• Label: 52.10.e
• Level: $52$
• Weight: $10$
• Character orbit: 52.e
• Rep. character: $\chi_{52}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $22$
• Newform subspaces: $1$
• Sturm bound: $70$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	52.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(70\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(52, [\chi])\).

	Total	New	Old
Modular forms	132	22	110
Cusp forms	120	22	98
Eisenstein series	12	0	12

Trace form

22 * q + 1558 * q^5 - 912 * q^7 - 86141 * q^9 - 62356 * q^11 - 123061 * q^13 + 261680 * q^15 - 287385 * q^17 + 972296 * q^19 - 4697572 * q^21 + 1364704 * q^23 + 14451564 * q^25 + 959040 * q^27 - 3519389 * q^29 + 261064 * q^31 + 9468338 * q^33 - 6981332 * q^35 + 3177215 * q^37 + 28026516 * q^39 + 9973683 * q^41 + 49893936 * q^43 - 133679627 * q^45 - 104211856 * q^47 - 58716657 * q^49 + 169736096 * q^51 + 421287990 * q^53 - 121162668 * q^55 + 278005700 * q^57 + 110701516 * q^59 - 204300861 * q^61 - 517552260 * q^63 + 85746941 * q^65 + 155800060 * q^67 + 51095526 * q^69 - 412154404 * q^71 - 1087762474 * q^73 + 394992808 * q^75 + 295319372 * q^77 + 520614392 * q^79 - 1057162619 * q^81 - 1787028048 * q^83 - 55108481 * q^85 + 717643380 * q^87 + 1110542628 * q^89 - 398885816 * q^91 - 111195960 * q^93 + 180320160 * q^95 + 1297775188 * q^97 + 5583384088 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(52, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
52.10.e.a	$52$	$10$	52.e	13.c	$3$	$22$	$11$	$26.782$		None		✓	✓	✓	52.10.e.a	$2$	$0$	\(0\)	\(0\)	\(1558\)	\(-912\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{10}^{\mathrm{old}}(52, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(52, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)