Space of modular forms of level 14 and weight 12

• Label: 14.12
• Level: 14
• Weight: 12
• Dimension: 22
• Nonzero newspaces: 2
• Newform subspaces: 6
• Sturm bound: 144
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(14))\).

	Total	New	Old
Modular forms	72	22	50
Cusp forms	60	22	38
Eisenstein series	12	0	12

Trace form

22 * q - 486 * q^3 - 2048 * q^4 + 15186 * q^5 - 46656 * q^6 + 68104 * q^7 - 390558 * q^9 - 245184 * q^10 + 2457060 * q^11 - 497664 * q^12 + 591230 * q^13 + 3729984 * q^14 + 7480968 * q^15 - 2097152 * q^16 + 8491944 * q^17 + 20198784 * q^18 - 12947098 * q^19 - 19200000 * q^20 - 58075194 * q^21 + 45078144 * q^22 + 113427624 * q^23 + 4521984 * q^24 - 231087650 * q^25 - 40719936 * q^26 + 75264156 * q^27 - 65282048 * q^28 - 105720120 * q^29 - 90244992 * q^30 + 496694996 * q^31 - 565250088 * q^33 - 545225088 * q^34 - 1430283750 * q^35 + 1527343104 * q^36 + 744915872 * q^37 + 1337082048 * q^38 + 2420822136 * q^39 - 251068416 * q^40 - 6090899760 * q^41 - 2501097408 * q^42 + 3064284116 * q^43 + 2516029440 * q^44 + 13053905202 * q^45 - 1938731136 * q^46 - 4893807348 * q^47 - 509607936 * q^48 - 14146151690 * q^49 - 1131447936 * q^50 + 20714441508 * q^51 + 3081820160 * q^52 - 1137524340 * q^53 - 9058717440 * q^54 - 31637889288 * q^55 - 3897360384 * q^56 + 5855275044 * q^57 + 16191398016 * q^58 + 21363358110 * q^59 + 4934025216 * q^60 - 26861288566 * q^61 - 42826630272 * q^62 - 19870263300 * q^63 + 23622320128 * q^64 + 50251750164 * q^65 + 8196298752 * q^66 + 18128698208 * q^67 + 8695750656 * q^68 - 45997267248 * q^69 - 11664695616 * q^70 + 11420507736 * q^71 + 20683554816 * q^72 + 77039951756 * q^73 - 4965307776 * q^74 + 776996574 * q^75 + 30729893888 * q^76 + 5462907996 * q^77 - 86764972032 * q^78 - 90454974808 * q^79 + 15923675136 * q^80 + 11588815578 * q^81 + 8393560704 * q^82 + 129680135670 * q^83 + 39467071488 * q^84 - 15485470380 * q^85 - 5974387584 * q^86 - 377918246484 * q^87 - 23353098240 * q^88 + 171490559604 * q^89 + 224543131968 * q^90 + 167978373062 * q^91 - 73887178752 * q^92 - 458471993040 * q^93 - 150177557760 * q^94 - 86426478168 * q^95 + 4630511616 * q^96 + 367531905752 * q^97 + 347442899712 * q^98 + 129769477356 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.12.a	\(\chi_{14}(1, \cdot)\)	14.12.a.a	1	1
		14.12.a.b	1
		14.12.a.c	2
		14.12.a.d	2
14.12.c	\(\chi_{14}(9, \cdot)\)	14.12.c.a	8	2
		14.12.c.b	8

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)