Space of modular forms of level 675 and weight 5

• Label: 675.5
• Level: 675
• Weight: 5
• Dimension: 46861
• Nonzero newspaces: 18
• Sturm bound: 162000
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(162000\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(675))\).

	Total	New	Old
Modular forms	65640	47517	18123
Cusp forms	63960	46861	17099
Eisenstein series	1680	656	1024

Trace form

46861 * q - 51 * q^2 - 78 * q^3 - 121 * q^4 - 64 * q^5 - 30 * q^6 - 11 * q^7 - 185 * q^8 - 180 * q^9 + 16 * q^10 - 431 * q^11 - 411 * q^12 + 761 * q^13 + 2227 * q^14 - 96 * q^15 - 745 * q^16 - 1857 * q^17 + 531 * q^18 - 2176 * q^19 - 1472 * q^20 - 2904 * q^21 + 351 * q^22 + 1950 * q^23 - 3384 * q^24 + 2064 * q^25 + 8096 * q^26 + 1296 * q^27 + 4458 * q^28 + 6016 * q^29 - 96 * q^30 - 1661 * q^31 + 8505 * q^32 + 17373 * q^33 + 4755 * q^34 + 980 * q^35 - 17040 * q^36 - 12438 * q^37 - 61031 * q^38 - 33855 * q^39 - 17472 * q^40 - 25091 * q^41 - 22098 * q^42 - 14833 * q^43 - 4553 * q^44 + 5244 * q^45 + 9521 * q^46 + 32235 * q^47 + 48345 * q^48 + 44047 * q^49 + 68216 * q^50 + 20562 * q^51 + 86403 * q^52 + 78552 * q^53 + 25326 * q^54 + 8872 * q^55 - 17927 * q^56 - 35760 * q^57 - 65613 * q^58 - 26459 * q^59 - 15648 * q^60 - 11399 * q^61 + 14264 * q^62 + 21537 * q^63 - 68831 * q^64 - 62416 * q^65 + 11229 * q^66 - 34402 * q^67 - 160846 * q^68 - 26919 * q^69 - 66960 * q^70 - 18317 * q^71 + 20652 * q^72 + 105321 * q^73 + 286743 * q^74 + 46272 * q^75 + 22935 * q^76 - 13969 * q^77 - 129300 * q^78 - 76813 * q^79 - 45232 * q^80 - 163248 * q^81 - 209322 * q^82 - 227109 * q^83 - 243756 * q^84 - 14896 * q^85 - 253667 * q^86 + 2883 * q^87 - 29673 * q^88 + 39724 * q^89 + 40716 * q^90 + 78473 * q^91 + 361293 * q^92 + 197061 * q^93 + 322923 * q^94 + 213628 * q^95 + 280086 * q^96 + 172800 * q^97 + 599758 * q^98 + 72723 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(675))\)

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
675.5.c	\(\chi_{675}(26, \cdot)\)	675.5.c.a	1	1
		675.5.c.b	1
		675.5.c.c	1
		675.5.c.d	2
		675.5.c.e	2
		675.5.c.f	2
		675.5.c.g	2
		675.5.c.h	2
		675.5.c.i	2
		675.5.c.j	4
		675.5.c.k	4
		675.5.c.l	4
		675.5.c.m	6
		675.5.c.n	6
		675.5.c.o	6
		675.5.c.p	6
		675.5.c.q	6
		675.5.c.r	10
		675.5.c.s	10
		675.5.c.t	12
		675.5.c.u	12
675.5.d	\(\chi_{675}(674, \cdot)\)	675.5.d.a	2	1
		675.5.d.b	2
		675.5.d.c	2
		675.5.d.d	2
		675.5.d.e	4
		675.5.d.f	4
		675.5.d.g	4
		675.5.d.h	8
		675.5.d.i	10
		675.5.d.j	10
		675.5.d.k	12
		675.5.d.l	12
		675.5.d.m	12
		675.5.d.n	12
675.5.g	\(\chi_{675}(82, \cdot)\)	n/a	192	2
675.5.i	\(\chi_{675}(224, \cdot)\)	n/a	140	2
675.5.j	\(\chi_{675}(251, \cdot)\)	n/a	146	2
675.5.m	\(\chi_{675}(134, \cdot)\)	n/a	640	4
675.5.o	\(\chi_{675}(161, \cdot)\)	n/a	640	4
675.5.p	\(\chi_{675}(118, \cdot)\)	n/a	280	4
675.5.s	\(\chi_{675}(74, \cdot)\)	n/a	1284	6
675.5.t	\(\chi_{675}(101, \cdot)\)	n/a	1350	6
675.5.v	\(\chi_{675}(28, \cdot)\)	n/a	1280	8
675.5.x	\(\chi_{675}(71, \cdot)\)	n/a	944	8
675.5.z	\(\chi_{675}(44, \cdot)\)	n/a	944	8
675.5.bb	\(\chi_{675}(7, \cdot)\)	n/a	2568	12
675.5.be	\(\chi_{675}(37, \cdot)\)	n/a	1888	16
675.5.bf	\(\chi_{675}(11, \cdot)\)	n/a	8592	24
675.5.bh	\(\chi_{675}(14, \cdot)\)	n/a	8592	24
675.5.bj	\(\chi_{675}(13, \cdot)\)	n/a	17184	48

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(675))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(675)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)