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

• Label: 1450.2.bn
• Level: $1450$
• Weight: $2$
• Character orbit: 1450.bn
• Rep. character: $\chi_{1450}(3,\cdot)$
• Character field: $\Q(\zeta_{140})$
• Dimension: $3600$
• Sturm bound: $450$

Defining parameters

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.bn (of order \(140\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 725 \)
Character field:			\(\Q(\zeta_{140})\)
Sturm bound:			\(450\)

Dimensions

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

	Total	New	Old
Modular forms	10992	3600	7392
Cusp forms	10608	3600	7008
Eisenstein series	384	0	384

Trace form

3600 * q - 150 * q^4 + 150 * q^9 + 10 * q^10 - 38 * q^13 + 150 * q^16 + 40 * q^19 - 30 * q^25 + 60 * q^26 - 300 * q^27 + 40 * q^29 - 20 * q^31 + 4 * q^33 + 40 * q^35 - 150 * q^36 - 42 * q^37 - 28 * q^38 - 10 * q^40 - 50 * q^41 + 32 * q^42 + 120 * q^43 + 40 * q^45 - 36 * q^47 - 40 * q^50 - 18 * q^52 - 208 * q^53 - 32 * q^55 - 48 * q^57 - 2 * q^58 - 92 * q^60 + 470 * q^61 + 136 * q^63 - 150 * q^64 + 16 * q^65 + 16 * q^67 - 48 * q^70 - 52 * q^73 + 208 * q^75 + 244 * q^77 + 152 * q^78 - 80 * q^79 + 150 * q^81 + 34 * q^82 + 56 * q^83 + 60 * q^84 - 8 * q^85 - 76 * q^87 + 20 * q^89 + 178 * q^90 - 52 * q^93 + 456 * q^95 + 12 * q^97 + 366 * 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

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