Space of modular forms of level 1040, weight 6, and Character 1040.fd

• Label: 1040.6.fd
• Level: $1040$
• Weight: $6$
• Character orbit: 1040.fd
• Rep. character: $\chi_{1040}(197,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $3344$
• Sturm bound: $1008$

Defining parameters

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1040.fd (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1040 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1040, [\chi])\).

	Total	New	Old
Modular forms	3376	3376	0
Cusp forms	3344	3344	0
Eisenstein series	32	32	0

Trace form

3344 * q - 2 * q^2 - 8 * q^5 - 8 * q^6 - 8 * q^8 + 134136 * q^9 + 562 * q^10 - 12 * q^11 - 1584 * q^12 - 8 * q^15 + 2276 * q^16 - 12 * q^17 - 972 * q^18 + 7502 * q^20 - 2504 * q^22 + 7108 * q^24 + 6832 * q^26 - 6 * q^28 - 6128 * q^30 - 16 * q^31 + 12788 * q^32 - 4 * q^33 + 8848 * q^34 + 18748 * q^35 + 25508 * q^36 - 4 * q^37 + 128 * q^38 - 1944 * q^39 + 59232 * q^40 + 43336 * q^42 - 12 * q^43 - 30280 * q^44 + 17772 * q^45 - 8 * q^46 + 167584 * q^48 - 3899224 * q^49 + 84346 * q^50 - 73594 * q^52 - 16 * q^53 - 33436 * q^54 - 37500 * q^55 - 12 * q^56 - 76462 * q^58 + 14480 * q^59 - 310460 * q^60 - 4 * q^61 + 51572 * q^62 + 134452 * q^63 - 27696 * q^65 - 16 * q^66 - 8 * q^67 - 134720 * q^68 + 119964 * q^70 + 195630 * q^72 - 98088 * q^75 - 56792 * q^76 + 382672 * q^78 + 459874 * q^80 - 10550096 * q^81 - 153342 * q^82 - 126432 * q^83 - 178724 * q^84 - 6256 * q^85 - 492788 * q^86 - 1944 * q^87 + 993170 * q^88 + 368064 * q^90 + 329432 * q^91 - 4104 * q^92 + 1940 * q^93 + 384 * q^94 - 12 * q^95 + 27552 * q^96 - 4 * q^97 - 905474 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(1040, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.