Space of modular forms of level 11, weight 12, and trivial character

• Label: 11.12.a
• Level: $11$
• Weight: $12$
• Character orbit: 11.a
• Rep. character: $\chi_{11}(1,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(11))\).

	Total	New	Old
Modular forms	12	8	4
Cusp forms	10	8	2
Eisenstein series	2	0	2

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

\(11\)	Dim
\(+\)	\(5\)
\(-\)	\(3\)

Trace form

8 * q + 32 * q^2 - 233 * q^3 + 9076 * q^4 - 15703 * q^5 + 10942 * q^6 + 73958 * q^7 - 56676 * q^8 + 307703 * q^9 + 449510 * q^10 - 322102 * q^11 + 1431584 * q^12 + 1964714 * q^13 + 1988732 * q^14 - 2772689 * q^15 + 3418600 * q^16 + 16395044 * q^17 - 20821822 * q^18 - 19590492 * q^19 + 6760168 * q^20 + 17398534 * q^21 - 5153632 * q^22 - 94440641 * q^23 - 83441748 * q^24 + 44566651 * q^25 - 125238196 * q^26 + 209008465 * q^27 + 200526736 * q^28 - 476100402 * q^29 + 240810694 * q^30 + 371580791 * q^31 + 908210584 * q^32 - 89061203 * q^33 - 1102433800 * q^34 + 254817638 * q^35 - 653073836 * q^36 + 422778399 * q^37 + 534201048 * q^38 + 1255438660 * q^39 - 1542772332 * q^40 + 504799778 * q^41 - 1024191356 * q^42 - 49493922 * q^43 - 541775564 * q^44 - 5756032 * q^45 + 472149670 * q^46 - 4355376128 * q^47 - 3141381208 * q^48 + 2557152516 * q^49 - 4723225718 * q^50 + 8840429458 * q^51 - 1951902872 * q^52 + 4727609532 * q^53 - 5957610494 * q^54 + 176028743 * q^55 + 7812077208 * q^56 + 6252115680 * q^57 + 11275380132 * q^58 + 5320998277 * q^59 - 5610203728 * q^60 - 26469446814 * q^61 + 16803218966 * q^62 - 12584866468 * q^63 + 6698319968 * q^64 + 5207837360 * q^65 + 448688086 * q^66 + 33465935785 * q^67 + 2291826712 * q^68 + 5424714107 * q^69 - 53189453716 * q^70 - 49169436051 * q^71 - 46682928432 * q^72 + 10272916070 * q^73 - 21440089350 * q^74 + 35944240640 * q^75 + 109723150848 * q^76 - 13547932222 * q^77 - 99909542648 * q^78 + 36156478486 * q^79 + 2843409976 * q^80 - 127998534496 * q^81 + 88813826300 * q^82 - 41341594746 * q^83 + 70613000912 * q^84 + 89181763862 * q^85 + 170675303052 * q^86 + 30444967224 * q^87 - 79988878068 * q^88 - 123823053765 * q^89 + 336287620112 * q^90 - 9388521112 * q^91 - 416009937424 * q^92 + 1013667979 * q^93 - 109248658064 * q^94 + 67395785832 * q^95 + 153846148520 * q^96 + 162861068113 * q^97 + 310631219304 * q^98 - 113395848049 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(11))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11
11.12.a.a	$11$	$12$	11.a	1.a	$1$	$3$	$3$	$8.452$	3.3.202533.1	None	✓	✓	✓	✓	11.12.a.a	$1$	$1$	\(0\)	\(-393\)	\(-7305\)	\(-5082\)		$-$	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-131-2\beta _{1}-4\beta _{2})q^{3}+\cdots\)
11.12.a.b	$11$	$12$	11.a	1.a	$1$	$5$	$5$	$8.452$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓	✓	11.12.a.b	$1$	$0$	\(32\)	\(160\)	\(-8398\)	\(79040\)		$+$	$+$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(6+\beta _{1})q^{2}+(2^{5}-\beta _{3})q^{3}+(1239+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(11))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(11)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)