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

• Label: 450.4.e
• Level: $450$
• Weight: $4$
• Character orbit: 450.e
• Rep. character: $\chi_{450}(151,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $114$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	450.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(360\)

Dimensions

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

	Total	New	Old
Modular forms	564	114	450
Cusp forms	516	114	402
Eisenstein series	48	0	48

Trace form

114 * q + 2 * q^2 - 5 * q^3 - 228 * q^4 - 2 * q^6 + 12 * q^7 - 16 * q^8 + 115 * q^9 + 11 * q^11 - 8 * q^12 - 24 * q^13 - 100 * q^14 - 912 * q^16 - 270 * q^17 + 140 * q^18 + 210 * q^19 + 196 * q^21 - 18 * q^22 + 96 * q^23 - 56 * q^24 + 232 * q^26 - 308 * q^27 - 96 * q^28 + 108 * q^29 + 66 * q^31 + 32 * q^32 - 783 * q^33 + 90 * q^34 - 476 * q^36 + 480 * q^37 + 346 * q^38 + 882 * q^39 - 763 * q^41 + 664 * q^42 + 129 * q^43 - 88 * q^44 - 504 * q^46 - 288 * q^47 + 112 * q^48 - 2835 * q^49 + 463 * q^51 - 96 * q^52 - 1848 * q^53 + 646 * q^54 - 400 * q^56 - 2173 * q^57 - 252 * q^58 - 1133 * q^59 + 822 * q^61 + 304 * q^62 + 3338 * q^63 + 7296 * q^64 - 148 * q^66 + 363 * q^67 + 540 * q^68 - 1754 * q^69 + 7032 * q^71 + 104 * q^72 - 258 * q^73 - 16 * q^74 - 420 * q^76 + 1812 * q^77 - 2540 * q^78 + 642 * q^79 - 2825 * q^81 + 828 * q^82 + 690 * q^83 + 376 * q^84 + 446 * q^86 + 6612 * q^87 - 72 * q^88 + 5564 * q^89 + 492 * q^91 + 384 * q^92 + 1106 * q^93 - 612 * q^94 + 256 * q^96 - 2067 * q^97 - 372 * q^98 + 1058 * 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

\( S_{4}^{\mathrm{old}}(450, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)