Space of modular forms of level 112 and weight 7

• Label: 112.7
• Level: 112
• Weight: 7
• Dimension: 1219
• Nonzero newspaces: 8
• Sturm bound: 5376
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(5376\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(112))\).

	Total	New	Old
Modular forms	2388	1265	1123
Cusp forms	2220	1219	1001
Eisenstein series	168	46	122

Trace form

1219 * q - 8 * q^2 - 5 * q^3 - 188 * q^4 + 121 * q^5 + 1012 * q^6 - 5 * q^7 - 1952 * q^8 - 1305 * q^9 + 2236 * q^10 - 2725 * q^11 + 4684 * q^12 + 7516 * q^13 - 7576 * q^14 - 18 * q^15 + 15940 * q^16 - 27871 * q^17 + 3736 * q^18 + 7243 * q^19 + 33116 * q^20 + 6077 * q^21 - 50528 * q^22 + 52951 * q^23 + 65172 * q^24 - 34197 * q^25 - 117916 * q^26 - 71564 * q^27 - 45188 * q^28 + 123362 * q^29 - 16916 * q^30 - 110889 * q^31 + 79332 * q^32 - 74179 * q^33 + 105164 * q^34 + 283627 * q^35 + 276944 * q^36 + 232369 * q^37 + 374548 * q^38 - 715108 * q^39 - 330332 * q^40 - 98604 * q^41 - 913380 * q^42 + 426874 * q^43 - 314244 * q^44 + 491814 * q^45 + 580976 * q^46 + 188487 * q^47 + 1001436 * q^48 + 2042131 * q^49 + 126824 * q^50 - 1178985 * q^51 - 478232 * q^52 - 666439 * q^53 - 338452 * q^54 + 465392 * q^55 + 405104 * q^56 + 1935930 * q^57 - 846416 * q^58 + 586299 * q^59 - 254212 * q^60 - 1291463 * q^61 + 980760 * q^62 - 30009 * q^63 - 789284 * q^64 + 75184 * q^65 + 1195252 * q^66 + 295459 * q^67 + 2251488 * q^68 + 618220 * q^69 + 2860804 * q^70 - 878298 * q^71 - 351476 * q^72 - 2288991 * q^73 - 7220804 * q^74 + 1362494 * q^75 - 8491988 * q^76 + 956229 * q^77 - 6358128 * q^78 + 2339055 * q^79 + 5797924 * q^80 + 3647966 * q^81 + 10009236 * q^82 + 576632 * q^83 + 7602764 * q^84 + 2304818 * q^85 + 6480940 * q^86 - 7814910 * q^87 - 6616316 * q^88 - 8171727 * q^89 - 19986940 * q^90 - 3963188 * q^91 - 9294116 * q^92 + 481609 * q^93 - 6047364 * q^94 + 11200383 * q^95 - 3249764 * q^96 + 2462708 * q^97 - 749860 * q^98 + 16643738 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(112))\)

We only show spaces with odd 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
112.7.c	\(\chi_{112}(97, \cdot)\)	112.7.c.a	1	1
		112.7.c.b	2
		112.7.c.c	4
		112.7.c.d	4
		112.7.c.e	12
112.7.d	\(\chi_{112}(15, \cdot)\)	112.7.d.a	6	1
		112.7.d.b	12
112.7.g	\(\chi_{112}(71, \cdot)\)	None	0	1
112.7.h	\(\chi_{112}(41, \cdot)\)	None	0	1
112.7.k	\(\chi_{112}(43, \cdot)\)	n/a	144	2
112.7.l	\(\chi_{112}(13, \cdot)\)	n/a	188	2
112.7.n	\(\chi_{112}(73, \cdot)\)	None	0	2
112.7.o	\(\chi_{112}(23, \cdot)\)	None	0	2
112.7.r	\(\chi_{112}(79, \cdot)\)	112.7.r.a	16	2
		112.7.r.b	16
		112.7.r.c	16
112.7.s	\(\chi_{112}(17, \cdot)\)	112.7.s.a	2	2
		112.7.s.b	4
		112.7.s.c	8
		112.7.s.d	8
		112.7.s.e	24
112.7.u	\(\chi_{112}(11, \cdot)\)	n/a	376	4
112.7.x	\(\chi_{112}(5, \cdot)\)	n/a	376	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(112))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(112)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)