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

• Label: 450.4.v
• Level: $450$
• Weight: $4$
• Character orbit: 450.v
• Rep. character: $\chi_{450}(79,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $720$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	450.v (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 225 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(360\)

Dimensions

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

	Total	New	Old
Modular forms	2192	720	1472
Cusp forms	2128	720	1408
Eisenstein series	64	0	64

Trace form

720 * q - 360 * q^4 - 32 * q^5 + 64 * q^9 + 44 * q^11 - 80 * q^12 - 112 * q^14 + 406 * q^15 + 1440 * q^16 - 32 * q^20 + 96 * q^21 - 576 * q^25 + 2496 * q^26 + 660 * q^27 - 348 * q^29 + 188 * q^30 - 72 * q^31 - 1600 * q^33 - 572 * q^35 + 512 * q^36 - 172 * q^39 + 656 * q^41 + 352 * q^44 + 1146 * q^45 + 1900 * q^47 + 640 * q^48 + 17640 * q^49 + 488 * q^50 - 68 * q^51 - 1104 * q^54 + 180 * q^55 + 448 * q^56 + 288 * q^59 - 1944 * q^60 - 4920 * q^62 - 5560 * q^63 + 11520 * q^64 - 1474 * q^65 - 544 * q^66 - 3060 * q^67 - 68 * q^69 - 144 * q^70 + 3064 * q^71 + 5920 * q^74 + 4878 * q^75 - 5440 * q^77 + 6640 * q^78 + 252 * q^79 - 256 * q^80 + 696 * q^81 + 280 * q^83 - 288 * q^84 - 828 * q^85 + 1720 * q^86 + 4200 * q^87 - 4528 * q^89 - 8524 * q^90 - 5680 * q^92 - 2772 * q^95 - 2848 * q^99

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

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