Space of modular forms of level 1200, weight 4, and Character 1200.bf

• Label: 1200.4.bf
• Level: $1200$
• Weight: $4$
• Character orbit: 1200.bf
• Rep. character: $\chi_{1200}(293,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $856$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1200.bf (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 240 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1200, [\chi])\).

	Total	New	Old
Modular forms	1464	872	592
Cusp forms	1416	856	560
Eisenstein series	48	16	32

Trace form

856 * q + 4 * q^3 + 24 * q^4 - 4 * q^6 + 56 * q^12 + 8 * q^13 + 256 * q^16 - 252 * q^18 + 48 * q^19 - 4 * q^21 + 188 * q^22 + 108 * q^24 + 4 * q^27 + 692 * q^28 - 16 * q^31 + 4 * q^33 - 1848 * q^34 - 260 * q^36 + 8 * q^37 - 216 * q^39 - 640 * q^42 + 160 * q^46 + 256 * q^48 - 4 * q^51 + 1136 * q^52 - 2112 * q^54 + 108 * q^57 - 2340 * q^58 - 1832 * q^61 + 1376 * q^63 - 3192 * q^64 - 3300 * q^66 + 108 * q^69 + 1608 * q^72 + 5200 * q^76 + 2172 * q^78 - 8 * q^81 - 1776 * q^82 - 6084 * q^84 - 108 * q^87 + 6132 * q^88 - 8 * q^91 + 112 * q^93 + 840 * q^94 - 2796 * q^96 + 8 * q^97 + 5312 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1200, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)