Space of modular forms of level 4, weight 26, and trivial character

• Label: 4.26.a
• Level: $4$
• Weight: $26$
• Character orbit: 4.a
• Rep. character: $\chi_{4}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $13$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$4 = 2^{2}$
Weight:	$k$	$=$	$26$
Character orbit:	$[\chi]$	$=$	4.a (trivial)
Character field:			$\Q$
Newform subspaces:			$1$
Sturm bound:			$13$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{26}(\Gamma_0(4))$.

	Total	New	Old
Modular forms	14	2	12
Cusp forms	11	2	9
Eisenstein series	3	0	3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$2$	Dim
$-$	$2$

Trace form

2 * q - 899640 * q^3 - 399350196 * q^5 - 40518462320 * q^7 + 848785998042 * q^9 - 1306289379240 * q^11 + 32729023492060 * q^13 + 1129212800709552 * q^15 + 4624697010380580 * q^17 + 24674021780774632 * q^19 + 114967389360140352 * q^21 - 31042927879759440 * q^23 - 94693927809381634 * q^25 - 1543594702580385840 * q^27 - 3328137384414404868 * q^29 - 6421803981270308288 * q^31 + 9385715601558142560 * q^33 + 51043698274430238048 * q^35 + 31687565809212923020 * q^37 + 49526653229543938032 * q^39 - 16316808963958618668 * q^41 - 341165113066738242920 * q^43 - 1023758965576016818596 * q^45 - 1118172622498866698400 * q^47 + 2514734995497417690354 * q^49 + 774064747141339317264 * q^51 + 7614510009160367483820 * q^53 + 4167198967582958322960 * q^55 - 4468294635852504762720 * q^57 - 4439075167218253907016 * q^59 - 10634755765830886628036 * q^61 - 104228162020256173326000 * q^63 + 21991306250852228329128 * q^65 - 27985598617668512548280 * q^67 + 308855371847014830833856 * q^69 - 31606985976821340133104 * q^71 + 390343645433421883811860 * q^73 - 336618576615723339381192 * q^75 + 424438601780393611266240 * q^77 - 1143923903407761106308704 * q^79 - 63792847020367292545422 * q^81 - 2544503743336324024143000 * q^83 + 343892775851675596114776 * q^85 + 579335111505652549849200 * q^87 + 3902025208165068648348468 * q^89 + 2243166387869650274782688 * q^91 + 9713299019180457972015360 * q^93 - 1982812931470769310151056 * q^95 - 8231826212771633749326140 * q^97 - 8469521205549833375650440 * q^99

Decomposition of $S_{26}^{\mathrm{new}}(\Gamma_0(4))$ 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
4.26.a.a	$4$	$26$	4.a	1.a	$1$	$2$	$2$	$15.840$	$\Q(\sqrt{358121})$	None	✓	✓	✓	✓	4.26.a.a	$1$	$0$	$0$	$-899640$	$-399350196$	$-40518462320$		$-$	$-$	$2^{7}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+(-449820-\beta )q^{3}+(-199675098+\cdots)q^{5}+\cdots$

Decomposition of $S_{26}^{\mathrm{old}}(\Gamma_0(4))$ into lower level spaces

$S_{26}^{\mathrm{old}}(\Gamma_0(4)) \simeq$ $S_{26}^{\mathrm{new}}(\Gamma_0(1))$$^{\oplus 3}$$\oplus$$S_{26}^{\mathrm{new}}(\Gamma_0(2))$$^{\oplus 2}$