Space of modular forms of level 14 and weight 4

• Label: 14.4
• Level: 14
• Weight: 4
• Dimension: 6
• Nonzero newspaces: 2
• Newform subspaces: 4
• Sturm bound: 48
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(14))\).

	Total	New	Old
Modular forms	24	6	18
Cusp forms	12	6	6
Eisenstein series	12	0	12

Trace form

6 * q + 12 * q^3 - 24 * q^5 - 36 * q^6 - 48 * q^7 + 42 * q^9 + 36 * q^10 + 42 * q^11 + 48 * q^12 + 66 * q^13 + 132 * q^14 - 12 * q^15 - 150 * q^17 - 168 * q^18 - 60 * q^19 - 120 * q^20 - 72 * q^21 - 216 * q^22 - 294 * q^23 - 48 * q^24 + 210 * q^25 + 348 * q^26 + 576 * q^27 + 120 * q^28 + 576 * q^29 + 168 * q^30 + 210 * q^31 - 570 * q^33 - 408 * q^34 - 420 * q^35 - 168 * q^36 + 42 * q^37 + 108 * q^38 - 252 * q^39 + 144 * q^40 - 792 * q^41 + 324 * q^42 - 516 * q^43 + 168 * q^44 - 78 * q^45 - 168 * q^46 - 18 * q^47 - 96 * q^48 - 90 * q^49 + 24 * q^50 + 1134 * q^51 + 312 * q^52 + 1302 * q^53 - 144 * q^54 + 1332 * q^55 + 48 * q^56 + 312 * q^57 - 504 * q^58 - 264 * q^59 - 504 * q^60 + 840 * q^61 + 120 * q^62 - 48 * q^63 + 384 * q^64 - 2016 * q^65 - 384 * q^66 - 2058 * q^67 - 600 * q^68 - 1332 * q^69 - 756 * q^70 - 792 * q^71 - 672 * q^72 - 594 * q^73 + 1512 * q^74 + 234 * q^75 + 1464 * q^76 + 2226 * q^77 + 1152 * q^78 + 1050 * q^79 - 384 * q^80 + 84 * q^81 - 984 * q^82 - 6 * q^83 - 912 * q^84 + 240 * q^85 + 840 * q^86 + 2304 * q^87 + 1344 * q^88 + 2310 * q^89 + 2388 * q^90 + 906 * q^91 - 432 * q^92 + 294 * q^93 - 816 * q^94 - 2058 * q^95 - 192 * q^96 - 4224 * q^97 - 2640 * q^98 - 3732 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.4.a	\(\chi_{14}(1, \cdot)\)	14.4.a.a	1	1
		14.4.a.b	1
14.4.c	\(\chi_{14}(9, \cdot)\)	14.4.c.a	2	2
		14.4.c.b	2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

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