LMFDB - Space of modular forms of level 11, weight 55, and Character 11.b

Defining parameters

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 55 $
Character orbit:	$[\chi]$	$=$	11.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 11 $
Character field:			$\Q$
Newform subspaces:			$ 2 $
Sturm bound:			$55$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{55}(11, [\chi])$.

	Total	New
Modular forms	55	55
Cusp forms	53	53
Eisenstein series	2	2

Trace form

$ 53 q - 10935593393726 q^{3} - 44\!\cdots\!96 q^{4} + 66\!\cdots\!94 q^{5} + 96\!\cdots\!19 q^{9} - 22\!\cdots\!15 q^{11} + 58\!\cdots\!36 q^{12} + 16\!\cdots\!92 q^{14} - 70\!\cdots\!60 q^{15} + 27\!\cdots\!60 q^{16}+ \cdots - 19\!\cdots\!89 q^{99}+O(q^{100}) $

53 * q - 10935593393726 * q^3 - 441934457578959196 * q^4 + 6661350309500469894 * q^5 + 966285863641244987977471819 * q^9 - 22104456690909433755171145515 * q^11 + 585983586501697639460077910836 * q^12 + 16430039554012313351203436359992 * q^14 - 70996808024541252697094105236660 * q^15 + 2742777150698862669595223332534760 * q^16 - 226674531889383261797422282801393764 * q^20 + 5157195751800922734792264208384329480 * q^22 + 1177078138377022351232708165673843114 * q^23 + 586395799149561999926842578790113216171 * q^25 - 23903626757343947450509876892108473848 * q^26 + 981662662038478481084204729250482569132 * q^27 - 7297019433702970551023960105640317647190 * q^31 - 78268443974618306376112842255521927402306 * q^33 - 382685645043240609705659970680557039229928 * q^34 - 4869107032614759578954220318159800394687392 * q^36 - 1375424051694408910707720714598481694636554 * q^37 + 6267023875339105181722396849401001675418280 * q^38 + 233752630869891611496131930259023024027708280 * q^42 + 190575638628902177214862515567462109504205292 * q^44 - 205799382701913227079888520238222476413352066 * q^45 + 1587654456840100917331735738700118629855045826 * q^47 - 21744264086460643679343306168318061794123516056 * q^48 - 22097008019445774275147220059812529925302077771 * q^49 + 211929437568504036675849946757811904659657478914 * q^53 + 184491545175789034889349860701123257404059274506 * q^55 - 115390777027518016965961806251106961752207578736 * q^56 + 123415413785221493914877502026401519729347314400 * q^58 + 491298726559540268596371653276751831163815979362 * q^59 - 2368630875150495435782697163149479881782922720180 * q^60 - 20234798485234530424937731166480404008592450029904 * q^64 - 12109964696898538496079641613985496397697206779640 * q^66 + 119586704500498782012631411946730199970657770891906 * q^67 - 58191175351797848440218062394713928797847473961544 * q^69 + 141378366598224342343682569243258760701305638203080 * q^70 - 162387785486836541856830456935389121645631391506934 * q^71 + 237587037224550087837776462400771681263017243062510 * q^75 + 2739497371467656838500502691014369701978070986696400 * q^77 - 3797303493019609112524351010578377144410143787250360 * q^78 + 8091564333747905794422125800141108559496300452736024 * q^80 - 1613330090851772043760994570868171010857980275865903 * q^81 + 8682266433343991868477433919286036680475470677409160 * q^82 - 18378905505542184123122315161672597532666950219110768 * q^86 - 204752719090322999381151475436422387978654598641242000 * q^88 - 150684493598476267820385408654037316603456210456886834 * q^89 + 458351954089278648241203301939015024423959292775141712 * q^91 - 225702179238366101899385408988692849700575238358451724 * q^92 + 375556648830080176449161051491637808648570324789586088 * q^93 + 444807409344531439516116150487041943891572582476973646 * q^97 - 1905547399841695503067894109339602459898402954545272689 * q^99

Decomposition of $S_{55}^{\mathrm{new}}(11, [\chi])$ 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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
11.55.b.a	$11$	$55$	11.b	11.b	$2$	$1$	$1$	$203.147$	$\Q$	$\Q(\sqrt{-11}) $	✓	✓			11.55.b.a	$2$	$0$	$0$	$15\!\cdots\!90$	$63\!\cdots\!74$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+15166324313290q^{3}+2^{54}q^{4}+\cdots$
11.55.b.b	$11$	$55$	11.b	11.b	$2$	$52$	$52$	$203.147$		None		✓	✓		11.55.b.b	$2$	$0$	$0$	$-26\!\cdots\!16$	$35\!\cdots\!20$	$0$		$\mathrm{SU}(2)[C_{2}]$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 55 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(55\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{55}^{\mathrm{new}}(11, [\chi])\) into newform subspaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	11.55.b

Level	$11$
Weight	$55$
Character orbit	11.b
Rep. character	$\chi_{11}(10,\cdot)$
Character field	$\Q$
Dimension	$53$
Newform subspaces	$2$
Sturm bound	$55$
Trace bound	$1$