Space of modular forms of level 1450, weight 2, and Character 1450.x

• Label: 1450.2.x
• Level: $1450$
• Weight: $2$
• Character orbit: 1450.x
• Rep. character: $\chi_{1450}(17,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $600$
• Sturm bound: $450$

Defining parameters

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.x (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 725 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(450\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1450, [\chi])\).

	Total	New	Old
Modular forms	1832	600	1232
Cusp forms	1768	600	1168
Eisenstein series	64	0	64

Trace form

600 * q - 2 * q^2 - 150 * q^4 - 2 * q^8 + 150 * q^9 + 18 * q^13 + 16 * q^15 - 150 * q^16 + 24 * q^17 - 40 * q^18 - 40 * q^19 + 2 * q^25 + 10 * q^26 + 60 * q^27 - 40 * q^29 - 20 * q^31 + 8 * q^32 + 4 * q^33 - 16 * q^35 + 150 * q^36 + 20 * q^37 - 28 * q^38 - 70 * q^41 + 32 * q^42 - 40 * q^45 - 100 * q^47 + 18 * q^50 + 18 * q^52 - 72 * q^53 - 16 * q^55 - 48 * q^57 + 12 * q^58 + 36 * q^60 - 70 * q^61 + 24 * q^63 - 150 * q^64 - 16 * q^65 + 16 * q^67 - 96 * q^68 - 68 * q^70 + 10 * q^72 + 52 * q^73 - 116 * q^75 - 120 * q^77 - 12 * q^78 + 80 * q^79 - 150 * q^81 - 34 * q^82 - 56 * q^83 - 60 * q^84 + 186 * q^85 - 144 * q^87 + 10 * q^89 + 44 * q^90 - 52 * q^93 + 48 * q^95 - 20 * q^97 - 80 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1450, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 2}\)