Space of modular forms of level 2450, weight 4, and Character 2450.bb

• Label: 2450.4.bb
• Level: $2450$
• Weight: $4$
• Character orbit: 2450.bb
• Rep. character: $\chi_{2450}(79,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $2400$
• Sturm bound: $1680$

Defining parameters

Level:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2450.bb (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(1680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2450, [\chi])\).

	Total	New	Old
Modular forms	10208	2400	7808
Cusp forms	9952	2400	7552
Eisenstein series	256	0	256

Trace form

2400 * q - 1200 * q^4 - 8 * q^5 + 48 * q^6 - 2700 * q^9 + 12 * q^10 + 84 * q^11 - 620 * q^15 + 4800 * q^16 + 640 * q^17 + 76 * q^19 - 64 * q^20 + 1440 * q^22 - 950 * q^23 - 384 * q^24 + 98 * q^25 + 1248 * q^26 + 2640 * q^27 + 192 * q^29 + 380 * q^30 + 414 * q^31 - 1600 * q^33 - 544 * q^34 - 21600 * q^36 + 1184 * q^39 - 48 * q^40 + 1888 * q^41 + 224 * q^44 + 1824 * q^45 - 1296 * q^46 - 2272 * q^50 - 588 * q^51 - 500 * q^53 + 864 * q^54 + 596 * q^55 + 216 * q^59 + 1360 * q^60 - 1388 * q^61 + 8400 * q^62 + 38400 * q^64 + 2926 * q^65 - 1600 * q^66 - 5904 * q^69 - 2600 * q^71 - 2280 * q^73 + 624 * q^74 + 5010 * q^75 - 2432 * q^76 - 2000 * q^79 - 128 * q^80 + 25636 * q^81 + 3180 * q^83 - 6604 * q^85 - 168 * q^86 + 1680 * q^88 - 1944 * q^89 + 20480 * q^90 + 4160 * q^92 + 1600 * q^94 - 9330 * q^95 - 384 * q^96 - 1860 * q^97 - 14512 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(2450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2450, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)