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

• Label: 1040.6.s
• Level: $1040$
• Weight: $6$
• Character orbit: 1040.s
• Rep. character: $\chi_{1040}(437,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $1672$
• Sturm bound: $1008$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	1688	1688	0
Cusp forms	1672	1672	0
Eisenstein series	16	16	0

Trace form

1672 * q - 4 * q^6 - 134136 * q^9 + 568 * q^10 - 8 * q^11 + 792 * q^12 - 4 * q^15 - 8 * q^16 - 132 * q^18 + 1360 * q^20 - 8 * q^21 + 3368 * q^22 + 9052 * q^24 + 5076 * q^26 + 4092 * q^28 + 12628 * q^30 - 8 * q^31 + 4488 * q^34 - 4 * q^35 - 51040 * q^36 - 4 * q^37 + 128 * q^38 + 1944 * q^39 - 59244 * q^40 + 968 * q^42 + 39960 * q^44 - 12504 * q^45 - 4 * q^46 - 8 * q^47 + 968 * q^48 - 3899224 * q^49 + 64168 * q^50 - 27972 * q^52 - 8 * q^53 + 33820 * q^54 + 1944 * q^57 - 4 * q^58 + 104396 * q^60 - 8 * q^61 - 103156 * q^62 - 27692 * q^65 - 8 * q^66 - 4 * q^67 - 281728 * q^68 + 116532 * q^70 - 131076 * q^72 + 20144 * q^73 - 96624 * q^75 + 64972 * q^76 - 141524 * q^78 + 314428 * q^80 + 10550072 * q^81 - 153336 * q^82 - 126444 * q^83 + 313180 * q^84 - 4 * q^85 - 270904 * q^86 + 1944 * q^87 + 108320 * q^88 - 184032 * q^90 + 164716 * q^91 + 4092 * q^92 - 976 * q^93 + 241896 * q^96 + 1102740 * q^98 + 341464 * 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.