Space of modular forms of level 1900, weight 4, and Character 1900.cd

• Label: 1900.4.cd
• Level: $1900$
• Weight: $4$
• Character orbit: 1900.cd
• Rep. character: $\chi_{1900}(43,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $6432$
• Sturm bound: $1200$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1900.cd (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 380 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1900, [\chi])\).

	Total	New	Old
Modular forms	10944	6528	4416
Cusp forms	10656	6432	4224
Eisenstein series	288	96	192

Trace form

6432 * q + 12 * q^2 + 48 * q^6 + 6 * q^8 + 6 * q^12 + 24 * q^13 + 768 * q^16 + 24 * q^17 + 24 * q^18 - 48 * q^21 + 60 * q^22 - 1644 * q^26 + 1536 * q^28 - 498 * q^32 + 348 * q^33 + 2568 * q^36 + 48 * q^37 - 1602 * q^38 + 1728 * q^41 + 1308 * q^42 - 12 * q^46 + 6144 * q^48 + 12 * q^52 + 24 * q^53 - 48 * q^56 + 24 * q^57 + 8232 * q^58 - 48 * q^61 - 6360 * q^62 - 2616 * q^66 + 6 * q^68 + 14424 * q^72 + 24 * q^73 - 3912 * q^76 - 2232 * q^77 + 486 * q^78 - 48 * q^81 + 10332 * q^82 - 16656 * q^86 + 6150 * q^88 - 9228 * q^92 + 348 * q^93 + 37008 * q^96 + 24 * q^97 - 1998 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1900, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)