Space of modular forms of level 2450, weight 2, and Character 2450.bp

• Label: 2450.2.bp
• Level: $2450$
• Weight: $2$
• Character orbit: 2450.bp
• Rep. character: $\chi_{2450}(13,\cdot)$
• Character field: $\Q(\zeta_{140})$
• Dimension: $6720$
• Sturm bound: $840$

Defining parameters

Level:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2450.bp (of order \(140\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1225 \)
Character field:			\(\Q(\zeta_{140})\)
Sturm bound:			\(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2450, [\chi])\).

	Total	New	Old
Modular forms	20352	6720	13632
Cusp forms	19968	6720	13248
Eisenstein series	384	0	384

Trace form

6720 * q - 8 * q^7 - 44 * q^15 - 280 * q^16 + 112 * q^17 + 20 * q^22 - 8 * q^23 + 8 * q^25 - 12 * q^28 + 24 * q^30 - 28 * q^35 - 280 * q^36 + 24 * q^37 + 112 * q^42 + 104 * q^43 + 448 * q^45 + 84 * q^47 + 32 * q^50 + 100 * q^53 - 84 * q^55 + 68 * q^57 + 80 * q^58 + 100 * q^63 + 32 * q^67 + 28 * q^70 + 84 * q^75 + 144 * q^77 + 80 * q^78 - 280 * q^81 + 840 * q^83 - 360 * q^84 - 40 * q^85 + 28 * q^87 + 8 * q^88 + 700 * q^89 - 336 * q^90 - 8 * q^92 - 20 * q^93 + 56 * q^95 + 32 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

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