Space of modular forms of level 2 and weight 14

• Label: 2.14
• Level: 2
• Weight: 14
• Dimension: 2
• Nonzero newspaces: 1
• Newform subspaces: 2
• Sturm bound: 3
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 2 \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(3\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(2))\).

	Total	New	Old
Modular forms	4	2	2
Cusp forms	2	2	0
Eisenstein series	2	0	2

Trace form

2 * q - 600 * q^3 + 8192 * q^4 - 53460 * q^5 + 196608 * q^6 - 369200 * q^7 + 1709946 * q^9 - 3932160 * q^10 + 4084344 * q^11 - 2457600 * q^12 - 2845700 * q^13 + 31850496 * q^14 - 78333840 * q^15 + 33554432 * q^16 + 131681700 * q^17 - 117964800 * q^18 - 106794680 * q^19 - 218972160 * q^20 + 875171904 * q^21 + 54067200 * q^22 - 1792659600 * q^23 + 805306368 * q^24 + 875016350 * q^25 + 1210318848 * q^26 - 2387545200 * q^27 - 1512243200 * q^28 + 4368056220 * q^29 - 4075683840 * q^30 + 2771239744 * q^31 + 72309600 * q^33 + 674758656 * q^34 - 5419522080 * q^35 + 7003938816 * q^36 - 22590929300 * q^37 + 24286003200 * q^38 + 29901362352 * q^39 - 16106127360 * q^40 - 52429051116 * q^41 - 45848985600 * q^42 + 110529014200 * q^43 + 16729473024 * q^44 + 10916247420 * q^45 - 37149868032 * q^46 - 95668711200 * q^47 - 10066329600 * q^48 - 1788972366 * q^49 + 210213273600 * q^50 - 23310302256 * q^51 - 11655987200 * q^52 - 98507315700 * q^53 - 109972684800 * q^54 - 135126771120 * q^55 + 130459631616 * q^56 + 614902480800 * q^57 - 393550233600 * q^58 - 187535765160 * q^59 - 320855408640 * q^60 + 546582757084 * q^61 + 410871398400 * q^62 - 774303174000 * q^63 + 137438953472 * q^64 - 504887486040 * q^65 + 385287192576 * q^66 + 483821583400 * q^67 + 539368243200 * q^68 - 353798952768 * q^69 - 125487022080 * q^70 - 760208731056 * q^71 - 483183820800 * q^72 - 259603126700 * q^73 - 1061067423744 * q^74 + 4782613661400 * q^75 - 437431009280 * q^76 - 543756628800 * q^77 - 642839347200 * q^78 - 1748577467360 * q^79 - 896909967360 * q^80 - 4649287111758 * q^81 + 3006765465600 * q^82 + 7424547885000 * q^83 + 3584704118784 * q^84 - 3843735995880 * q^85 - 448279805952 * q^86 - 10755622472400 * q^87 + 221459251200 * q^88 + 6497185492980 * q^89 - 208691527680 * q^90 + 5231035901024 * q^91 - 7342733721600 * q^92 + 9029541638400 * q^93 - 734525128704 * q^94 - 8802659739600 * q^95 + 3298534883328 * q^96 + 3993560066500 * q^97 - 11759203123200 * q^98 + 2713436162712 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)

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
2.14.a	\(\chi_{2}(1, \cdot)\)	2.14.a.a	1	1
		2.14.a.b	1