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

• Label: 2450.2.h
• Level: $2450$
• Weight: $2$
• Character orbit: 2450.h
• Rep. character: $\chi_{2450}(491,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $412$
• Sturm bound: $840$

Defining parameters

Level:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2450.h (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(840\)

Dimensions

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

	Total	New	Old
Modular forms	1744	412	1332
Cusp forms	1616	412	1204
Eisenstein series	128	0	128

Trace form

412 * q - q^2 - 4 * q^3 - 103 * q^4 + 9 * q^5 + 2 * q^6 - q^8 - 109 * q^9 - q^10 - 8 * q^11 + 6 * q^12 - 14 * q^13 - 16 * q^15 - 103 * q^16 + 4 * q^17 + 28 * q^18 + 14 * q^19 + 4 * q^20 - 8 * q^22 - 14 * q^23 - 8 * q^24 + 49 * q^25 - 30 * q^26 + 8 * q^27 - 24 * q^29 - 12 * q^30 - 18 * q^31 + 4 * q^32 - 30 * q^33 + 19 * q^34 - 109 * q^36 + 17 * q^37 - 4 * q^38 + 8 * q^39 - q^40 - 16 * q^41 - 12 * q^43 + 2 * q^44 - 7 * q^45 - 16 * q^46 + 54 * q^47 + 6 * q^48 - 5 * q^50 + 8 * q^51 - 14 * q^52 + 43 * q^53 - 4 * q^54 + 46 * q^55 - 72 * q^57 - 22 * q^58 - 12 * q^59 + 4 * q^60 + 24 * q^61 - 44 * q^62 - 103 * q^64 + 57 * q^65 + 24 * q^66 + 66 * q^67 - 46 * q^68 - 16 * q^69 - 10 * q^71 + 3 * q^72 + 6 * q^73 + 2 * q^74 - 130 * q^75 - 16 * q^76 + 72 * q^78 + 48 * q^79 - q^80 - 93 * q^81 - 90 * q^82 - 54 * q^83 + 79 * q^85 + 2 * q^86 + 144 * q^87 + 2 * q^88 - 41 * q^89 - 87 * q^90 + 6 * q^92 + 36 * q^93 + 24 * q^94 - 4 * q^95 + 2 * q^96 + 2 * q^97 + 36 * q^99

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

\( S_{2}^{\mathrm{old}}(2450, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)