Space of modular forms of level 450, weight 4, and Character 450.w

• Label: 450.4.w
• Level: $450$
• Weight: $4$
• Character orbit: 450.w
• Rep. character: $\chi_{450}(23,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $1440$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	450.w (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 225 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(450, [\chi])\).

	Total	New	Old
Modular forms	4384	1440	2944
Cusp forms	4256	1440	2816
Eisenstein series	128	0	128

Trace form

1440 * q + 8 * q^3 - 32 * q^12 - 172 * q^15 - 2880 * q^16 - 16 * q^18 + 192 * q^20 + 312 * q^23 + 1152 * q^25 - 244 * q^27 - 336 * q^30 - 268 * q^33 + 288 * q^37 + 72 * q^38 + 2440 * q^39 + 952 * q^42 - 1008 * q^45 + 3444 * q^47 + 256 * q^48 + 672 * q^50 + 1584 * q^55 - 2504 * q^57 + 504 * q^58 - 9960 * q^59 - 1824 * q^60 - 4420 * q^63 - 696 * q^65 + 1224 * q^67 + 4608 * q^68 + 6160 * q^69 - 128 * q^72 + 6372 * q^75 + 22896 * q^77 + 6392 * q^78 - 1280 * q^81 - 3744 * q^82 + 2820 * q^83 - 960 * q^84 - 1656 * q^85 - 3248 * q^87 - 4792 * q^90 + 1248 * q^92 + 2004 * q^93 + 3540 * q^95 + 1512 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(450, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)