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

• Label: 1040.6.dp
• Level: $1040$
• Weight: $6$
• Character orbit: 1040.dp
• Rep. character: $\chi_{1040}(3,\cdot)$
• 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.dp (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 - 4 * q^3 - 8 * q^5 - 4 * q^6 - 4 * q^7 - 8 * q^8 - 134136 * q^9 + 62 * q^10 - 4 * q^11 - 620 * q^12 - 972 * q^15 - 4 * q^16 - 4 * q^17 + 1092 * q^18 - 2 * q^20 - 16 * q^21 + 2628 * q^22 - 4 * q^23 - 972 * q^24 + 872 * q^26 + 1928 * q^27 - 4098 * q^28 - 398 * q^30 - 12792 * q^32 - 4 * q^33 - 17440 * q^34 + 6248 * q^35 + 8188 * q^36 - 136 * q^38 - 53068 * q^40 + 44900 * q^42 - 70240 * q^44 - 5280 * q^45 - 4 * q^46 + 57156 * q^48 - 10092 * q^50 - 16 * q^51 + 73586 * q^52 - 16 * q^53 + 64340 * q^54 - 4 * q^55 - 4 * q^56 + 1944 * q^57 + 76710 * q^58 + 14480 * q^59 + 176648 * q^60 - 4 * q^61 + 32284 * q^62 - 972 * q^63 - 8 * q^65 + 34864 * q^66 + 134716 * q^68 + 1944 * q^69 - 199900 * q^70 + 287672 * q^71 - 64566 * q^72 - 20144 * q^73 - 84336 * q^74 - 97112 * q^75 + 121756 * q^76 + 134440 * q^77 - 413912 * q^78 - 164200 * q^80 - 10550096 * q^81 + 98222 * q^82 - 252896 * q^83 + 246924 * q^84 + 6248 * q^85 - 614416 * q^86 - 4 * q^87 + 75510 * q^88 + 388588 * q^90 - 329448 * q^91 + 932884 * q^92 - 204760 * q^95 + 663424 * q^96 - 4 * q^97 + 845562 * q^98 + 680984 * q^99

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

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