Space of modular forms of level 408, weight 4, and Character 408.bm

• Label: 408.4.bm
• Level: $408$
• Weight: $4$
• Character orbit: 408.bm
• Rep. character: $\chi_{408}(5,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $1696$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 408 = 2^{3} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	408.bm (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 408 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(408, [\chi])\).

	Total	New	Old
Modular forms	1760	1760	0
Cusp forms	1696	1696	0
Eisenstein series	64	64	0

Trace form

1696 * q - 16 * q^4 - 8 * q^6 - 32 * q^7 - 16 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^15 - 16 * q^18 - 16 * q^22 - 8 * q^24 - 32 * q^25 - 160 * q^28 - 8 * q^30 - 32 * q^31 + 3680 * q^34 - 8 * q^36 - 16 * q^39 + 560 * q^40 - 8 * q^42 - 1984 * q^46 - 224 * q^48 - 32 * q^49 - 32 * q^52 - 4608 * q^54 - 32 * q^55 - 1392 * q^57 - 16 * q^58 + 1136 * q^60 - 16 * q^63 - 16 * q^64 + 6688 * q^66 - 144 * q^70 + 4880 * q^72 - 32 * q^73 - 16 * q^76 - 4480 * q^78 - 32 * q^79 + 3664 * q^81 - 16 * q^82 - 16 * q^87 + 5168 * q^88 - 4728 * q^90 + 4304 * q^94 - 10800 * q^96 - 32 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(408, [\chi])\) into newform subspaces

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