Space of modular forms of level 10, weight 11, and Character 10.c

• Label: 10.11.c
• Level: $10$
• Weight: $11$
• Character orbit: 10.c
• Rep. character: $\chi_{10}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $16$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(16\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(10, [\chi])\).

	Total	New	Old
Modular forms	34	10	24
Cusp forms	26	10	16
Eisenstein series	8	0	8

Trace form

10 * q - 32 * q^2 - 124 * q^3 + 7560 * q^5 - 12160 * q^6 + 10604 * q^7 + 16384 * q^8 - 94880 * q^10 + 451520 * q^11 - 63488 * q^12 - 988434 * q^13 + 3637820 * q^15 - 2621440 * q^16 - 52906 * q^17 - 7111648 * q^18 + 4183040 * q^20 + 20016320 * q^21 - 13506304 * q^22 - 26934364 * q^23 + 51867350 * q^25 + 15915840 * q^26 - 53985640 * q^27 - 5429248 * q^28 + 12272640 * q^30 + 75553720 * q^31 + 8388608 * q^32 - 100984528 * q^33 - 194072740 * q^35 + 136186880 * q^36 + 78377634 * q^37 + 146994560 * q^38 + 6471680 * q^40 - 407745280 * q^41 - 72606464 * q^42 + 291961716 * q^43 - 329257430 * q^45 + 101491840 * q^46 + 877618884 * q^47 + 32505856 * q^48 - 1147160800 * q^50 + 663858520 * q^51 - 506078208 * q^52 + 59690386 * q^53 + 955263120 * q^55 + 269025280 * q^56 - 395251120 * q^57 + 468378880 * q^58 - 166942720 * q^60 + 709135920 * q^61 - 3714249344 * q^62 - 5999298844 * q^63 + 4317976170 * q^65 + 7842145280 * q^66 + 2285641604 * q^67 + 27087872 * q^68 - 1659966080 * q^70 - 7725259880 * q^71 - 3641163776 * q^72 - 4474810454 * q^73 + 8638494700 * q^75 + 5823385600 * q^76 + 4559799088 * q^77 + 14413532544 * q^78 - 1981808640 * q^80 - 23040515690 * q^81 - 13760829184 * q^82 - 7763146644 * q^83 - 1500700690 * q^85 + 13415015040 * q^86 + 44300553440 * q^87 + 6915227648 * q^88 - 32944166560 * q^90 - 32840264280 * q^91 - 13790394368 * q^92 + 22411006592 * q^93 + 3342839800 * q^95 + 3187671040 * q^96 + 30947240394 * q^97 + 23335064288 * q^98

Decomposition of \(S_{11}^{\mathrm{new}}(10, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.11.c.a	$10$	$11$	10.c	5.c	$4$	$2$	$1$	$6.354$	\(\Q(\sqrt{-1}) \)	None		✓			10.11.c.a	$2$	$0$	\(32\)	\(-366\)	\(-3750\)	\(-16814\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(16 i+16)q^{2}+(183 i-183)q^{3}+\cdots\)
10.11.c.b	$10$	$11$	10.c	5.c	$4$	$2$	$1$	$6.354$	\(\Q(\sqrt{-1}) \)	None		✓			10.11.c.b	$2$	$0$	\(32\)	\(114\)	\(5850\)	\(13906\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(16 i+16)q^{2}+(-57 i+57)q^{3}+\cdots\)
10.11.c.c	$10$	$11$	10.c	5.c	$4$	$6$	$3$	$6.354$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓	✓		10.11.c.c	$2$	$0$	\(-96\)	\(128\)	\(5460\)	\(13512\)	$2^{8}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{4}-2^{4}\beta _{1})q^{2}+(21-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(10, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)