Space of modular forms of level 7 and weight 14

• Label: 7.14
• Level: 7
• Weight: 14
• Dimension: 23
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 56
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 7 \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(56\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(7))\).

	Total	New	Old
Modular forms	29	27	2
Cusp forms	23	23	0
Eisenstein series	6	4	2

Trace form

23 * q - 3 * q^2 - 732 * q^3 - 16387 * q^4 + 47034 * q^5 - 279942 * q^6 + 375641 * q^7 - 49137 * q^8 + 2144115 * q^9 - 3412098 * q^10 + 6603396 * q^11 + 1933050 * q^12 - 28489118 * q^13 - 51732807 * q^14 + 222371112 * q^15 - 228808975 * q^16 - 187989666 * q^17 + 623979555 * q^18 + 717129484 * q^19 - 2329603584 * q^20 + 651643020 * q^21 + 921127140 * q^22 - 741101616 * q^23 - 551833566 * q^24 + 2859410201 * q^25 - 1882333404 * q^26 + 3079251912 * q^27 - 5077980859 * q^28 - 4754971182 * q^29 + 18343127094 * q^30 + 3272676256 * q^31 - 25747589553 * q^32 - 8070949704 * q^33 + 15740543646 * q^34 - 9377155242 * q^35 - 8971879335 * q^36 + 2546891554 * q^37 + 90115575672 * q^38 + 40364911440 * q^39 - 67719376080 * q^40 - 136444433706 * q^41 - 121501666314 * q^42 + 116999995060 * q^43 + 165542303556 * q^44 + 154934206650 * q^45 + 187496325630 * q^46 - 90083260560 * q^47 - 1048507061250 * q^48 - 182226639049 * q^49 + 361458218013 * q^50 + 915877635384 * q^51 + 1117861686844 * q^52 - 53497886622 * q^53 - 1248386893230 * q^54 - 651645370728 * q^55 - 1977873684465 * q^56 + 41832418752 * q^57 + 2830827074706 * q^58 + 2406993851580 * q^59 + 718098303804 * q^60 - 2028888278822 * q^61 - 4490748583704 * q^62 - 3496564250235 * q^63 + 1498258895585 * q^64 + 4780085827524 * q^65 + 9272361154374 * q^66 + 726018910948 * q^67 - 4151480070990 * q^68 - 11932165417968 * q^69 - 8497249945254 * q^70 + 5067748539816 * q^71 + 15311480453823 * q^72 + 7105467922990 * q^73 + 5070291270000 * q^74 - 11240309132652 * q^75 - 24376441034414 * q^76 - 6366309918276 * q^77 + 7312326116928 * q^78 + 12454092498040 * q^79 + 26389262427888 * q^80 + 8513196484959 * q^81 - 15528037464450 * q^82 - 19058763856356 * q^83 - 26915122244430 * q^84 + 6842311958340 * q^85 + 26480843462424 * q^86 + 25538752269120 * q^87 - 7665307122240 * q^88 - 5732241401298 * q^89 - 21195747882564 * q^90 - 13004660360258 * q^91 - 7903306557144 * q^92 + 23718439410888 * q^93 + 17597311757154 * q^94 - 17000176593408 * q^95 - 7675751295870 * q^96 + 23954043868174 * q^97 + 1361032641885 * q^98 - 9820452567852 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.14.a	\(\chi_{7}(1, \cdot)\)	7.14.a.a	3	1
		7.14.a.b	4
7.14.c	\(\chi_{7}(2, \cdot)\)	7.14.c.a	16	2