Space of modular forms of level 14 and weight 10

• Label: 14.10
• Level: 14
• Weight: 10
• Dimension: 16
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 120
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(14))\).

	Total	New	Old
Modular forms	60	16	44
Cusp forms	48	16	32
Eisenstein series	12	0	12

Trace form

16 * q - 32 * q^2 - 12 * q^3 - 512 * q^4 - 3444 * q^5 + 12768 * q^6 - 1784 * q^7 - 8192 * q^8 + 41388 * q^9 + 49056 * q^10 + 49506 * q^11 - 3072 * q^12 + 204410 * q^13 - 175904 * q^14 + 624372 * q^15 - 131072 * q^16 - 1171470 * q^17 - 849120 * q^18 + 892100 * q^19 + 514560 * q^20 - 61728 * q^21 + 775488 * q^22 - 6884358 * q^23 - 466944 * q^24 - 2449688 * q^25 - 1334944 * q^26 + 23712624 * q^27 + 3433984 * q^28 - 9160380 * q^29 - 18072192 * q^30 - 12681910 * q^31 - 2097152 * q^32 + 25482786 * q^33 + 23961216 * q^34 + 34021092 * q^35 + 29153280 * q^36 - 84667126 * q^37 - 49294432 * q^38 + 33234684 * q^39 + 12558336 * q^40 + 103079556 * q^41 + 50046432 * q^42 - 106746652 * q^43 + 12673536 * q^44 - 240131598 * q^45 - 41442432 * q^46 + 30612630 * q^47 + 31064064 * q^48 + 189121360 * q^49 - 53004704 * q^50 - 11940930 * q^51 - 37210624 * q^52 + 43182078 * q^53 - 126894528 * q^54 - 42579468 * q^55 + 28696576 * q^56 + 110895672 * q^57 + 94601856 * q^58 + 22747920 * q^59 + 147515904 * q^60 + 196941860 * q^61 + 44818496 * q^62 - 114794616 * q^63 + 268435456 * q^64 - 83308512 * q^65 - 22186752 * q^66 + 270031526 * q^67 - 299896320 * q^68 - 930360780 * q^69 - 590929248 * q^70 + 881132616 * q^71 - 217374720 * q^72 + 723010118 * q^73 + 516837248 * q^74 - 687736950 * q^75 - 418783744 * q^76 - 1135851402 * q^77 + 1155007488 * q^78 + 1119367706 * q^79 - 225705984 * q^80 - 737784798 * q^81 - 1298006784 * q^82 + 12360762 * q^83 - 1169058816 * q^84 - 540605688 * q^85 + 245645504 * q^86 + 332551368 * q^87 + 257310720 * q^88 + 61119390 * q^89 + 3590538528 * q^90 + 1594598498 * q^91 + 1484829696 * q^92 - 919222998 * q^93 - 367048512 * q^94 + 1274394246 * q^95 - 119537664 * q^96 - 4014782740 * q^97 - 2968313888 * q^98 - 981228444 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)

We only show spaces with even 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
14.10.a	\(\chi_{14}(1, \cdot)\)	14.10.a.a	1	1
		14.10.a.b	1
		14.10.a.c	2
14.10.c	\(\chi_{14}(9, \cdot)\)	14.10.c.a	6	2
		14.10.c.b	6

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)