Space of modular forms of level 400, weight 4, and Character 400.bl

• Label: 400.4.bl
• Level: $400$
• Weight: $4$
• Character orbit: 400.bl
• Rep. character: $\chi_{400}(29,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1424$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	400.bl (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 400 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(400, [\chi])\).

	Total	New	Old
Modular forms	1456	1456	0
Cusp forms	1424	1424	0
Eisenstein series	32	32	0

Trace form

1424 * q - 10 * q^2 - 10 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 + 200 * q^8 - 14 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 54 * q^14 - 16 * q^15 - 6 * q^16 - 20 * q^17 - 6 * q^19 - 162 * q^20 - 168 * q^21 - 10 * q^22 - 16 * q^24 + 4 * q^26 - 10 * q^27 - 650 * q^28 - 6 * q^29 - 746 * q^30 + 732 * q^31 - 20 * q^33 + 250 * q^34 - 1236 * q^35 - 922 * q^36 - 10 * q^37 + 3000 * q^38 - 1012 * q^40 - 2170 * q^42 - 804 * q^44 - 312 * q^45 + 26 * q^46 - 20 * q^47 + 6100 * q^48 + 65040 * q^49 - 350 * q^50 - 124 * q^51 - 3880 * q^52 - 10 * q^53 - 870 * q^54 - 2064 * q^56 - 10 * q^58 - 6 * q^59 + 12328 * q^60 - 6 * q^61 - 10 * q^62 - 6880 * q^63 - 2904 * q^64 + 1936 * q^65 + 3652 * q^66 - 4630 * q^67 + 102 * q^69 + 20 * q^70 - 10 * q^72 - 2172 * q^74 + 594 * q^75 - 3076 * q^76 - 3440 * q^77 - 10 * q^78 + 3148 * q^79 - 3554 * q^80 + 26232 * q^81 - 10 * q^83 - 6548 * q^84 - 258 * q^85 + 5554 * q^86 - 780 * q^88 - 642 * q^90 - 2064 * q^91 + 6920 * q^92 + 5490 * q^94 - 3880 * q^95 + 7734 * q^96 - 20 * q^97 - 3520 * q^98 - 3040 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(400, [\chi])\) into newform subspaces

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