Space of modular forms of level 19 and weight 11

• Label: 19.11
• Level: 19
• Weight: 11
• Dimension: 141
• Nonzero newspaces: 3
• Newform subspaces: 4
• Sturm bound: 330
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 19 \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(330\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(19))\).

	Total	New	Old
Modular forms	159	159	0
Cusp forms	141	141	0
Eisenstein series	18	18	0

Trace form

141 * q - 9 * q^2 - 9 * q^3 - 9 * q^4 - 9 * q^5 - 9 * q^6 - 9 * q^7 - 9 * q^8 - 9 * q^9 - 9 * q^10 - 9 * q^11 - 1493001 * q^12 + 1683291 * q^13 - 1837449 * q^14 - 2838735 * q^15 + 5621751 * q^16 + 2927502 * q^17 - 10958964 * q^19 - 20477970 * q^20 + 3801726 * q^21 + 31261239 * q^22 + 10149516 * q^23 - 22394889 * q^24 - 48982635 * q^25 - 26737929 * q^26 + 91704069 * q^27 - 90040326 * q^28 + 88955847 * q^29 + 219591972 * q^30 - 61388397 * q^31 - 294861384 * q^32 - 158021073 * q^33 + 186514506 * q^34 + 321628383 * q^35 + 674279217 * q^36 - 589570452 * q^38 - 789807150 * q^39 - 713461734 * q^40 + 12010383 * q^41 + 1436577741 * q^42 + 1400808696 * q^43 - 627224148 * q^44 - 436526154 * q^45 - 41114754 * q^46 + 84918888 * q^47 - 1319007006 * q^48 + 232421100 * q^49 - 939859668 * q^50 - 2980284048 * q^51 + 1177921527 * q^52 + 1850052843 * q^53 + 3334550184 * q^54 + 1529593587 * q^55 - 2211476364 * q^57 - 3029355666 * q^58 - 3942302274 * q^59 - 1505042892 * q^60 - 6786033729 * q^61 + 2098697940 * q^62 + 11874071187 * q^63 + 21670953999 * q^64 + 6677673336 * q^65 - 10127964897 * q^66 - 16708223442 * q^67 - 27106013664 * q^68 - 11104580178 * q^69 + 8608058307 * q^70 + 18062248212 * q^71 + 35313966252 * q^72 + 12143243940 * q^73 + 10219891167 * q^74 - 14233684419 * q^76 - 18815451975 * q^77 - 55791103599 * q^78 - 29585665239 * q^79 + 5065788303 * q^80 + 28148719077 * q^81 + 60210552978 * q^82 + 19966920606 * q^83 + 22806365931 * q^84 + 3212431875 * q^85 - 22200957666 * q^86 - 59437940769 * q^87 - 61125759153 * q^88 - 34340405364 * q^89 + 26700041376 * q^90 + 52629401739 * q^91 + 109381595850 * q^92 + 56378608803 * q^93 - 63861958638 * q^95 - 208890859338 * q^96 - 26793284616 * q^97 + 41994560808 * q^98 + 44372036601 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(19))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
19.11.b	\(\chi_{19}(18, \cdot)\)	19.11.b.a	1	1
		19.11.b.b	14
19.11.d	\(\chi_{19}(8, \cdot)\)	19.11.d.a	30	2
19.11.f	\(\chi_{19}(2, \cdot)\)	19.11.f.a	96	6