Space of modular forms of level 1800, weight 4, and Character 1800.do

• Label: 1800.4.do
• Level: $1800$
• Weight: $4$
• Character orbit: 1800.do
• Rep. character: $\chi_{1800}(77,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $17216$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1800.do (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1800 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1800, [\chi])\).

	Total	New	Old
Modular forms	17344	17344	0
Cusp forms	17216	17216	0
Eisenstein series	128	128	0

Trace form

17216 * q - 24 * q^2 - 10 * q^4 - 12 * q^6 - 16 * q^7 - 40 * q^9 - 32 * q^10 - 70 * q^12 - 30 * q^14 - 32 * q^15 - 6 * q^16 - 508 * q^18 - 24 * q^20 - 40 * q^22 - 48 * q^23 - 16 * q^25 + 224 * q^28 + 314 * q^30 - 12 * q^31 - 1404 * q^32 - 140 * q^33 - 10 * q^34 + 244 * q^36 + 24 * q^38 - 40 * q^39 - 8 * q^40 - 36 * q^41 - 1530 * q^42 - 24 * q^46 - 48 * q^47 + 5948 * q^48 - 24 * q^50 - 264 * q^52 - 3790 * q^54 - 1064 * q^55 - 18 * q^56 + 184 * q^57 + 24 * q^58 + 8102 * q^60 + 1340 * q^63 - 40 * q^64 - 48 * q^65 - 876 * q^66 + 360 * q^68 + 492 * q^70 + 3282 * q^72 - 64 * q^73 + 240 * q^76 - 5194 * q^78 - 20 * q^79 - 24 * q^81 - 20 * q^84 - 18 * q^86 - 1212 * q^87 + 3104 * q^88 + 4762 * q^90 - 9486 * q^92 - 8290 * q^94 + 1452 * q^95 - 12 * q^96 - 16 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

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