Space of modular forms of level 1950, weight 2, and Character 1950.cp

• Label: 1950.2.cp
• Level: $1950$
• Weight: $2$
• Character orbit: 1950.cp
• Rep. character: $\chi_{1950}(139,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $576$
• Sturm bound: $840$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.cp (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 325 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1950, [\chi])\).

	Total	New	Old
Modular forms	3424	576	2848
Cusp forms	3296	576	2720
Eisenstein series	128	0	128

Trace form

576 * q - 72 * q^4 - 72 * q^9 - 4 * q^15 + 72 * q^16 + 24 * q^19 + 40 * q^23 - 48 * q^25 - 8 * q^26 + 16 * q^29 - 20 * q^33 - 24 * q^34 + 20 * q^35 + 72 * q^36 + 44 * q^41 + 352 * q^49 - 8 * q^50 + 64 * q^51 + 160 * q^53 + 72 * q^55 + 24 * q^59 - 8 * q^60 + 32 * q^61 + 60 * q^62 + 144 * q^64 + 4 * q^65 - 32 * q^66 - 8 * q^69 + 128 * q^70 + 64 * q^71 + 160 * q^73 + 8 * q^74 + 8 * q^75 + 16 * q^76 - 160 * q^77 + 32 * q^79 + 72 * q^81 - 84 * q^85 + 48 * q^86 - 20 * q^87 - 24 * q^89 + 112 * q^91 - 16 * q^94 + 24 * q^95 + 80 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1950, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)