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

• Label: 1900.4.z
• Level: $1900$
• Weight: $4$
• Character orbit: 1900.z
• Rep. character: $\chi_{1900}(229,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $536$
• Sturm bound: $1200$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1900.z (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(1200\)

Dimensions

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

	Total	New	Old
Modular forms	3624	536	3088
Cusp forms	3576	536	3040
Eisenstein series	48	0	48

Trace form

536 * q - 16 * q^5 + 1106 * q^9 + 2 * q^11 + 156 * q^15 + 160 * q^17 - 38 * q^19 - 70 * q^23 - 732 * q^25 - 540 * q^27 + 272 * q^29 + 756 * q^31 + 1600 * q^33 + 242 * q^35 - 1360 * q^37 + 280 * q^39 + 400 * q^41 - 484 * q^45 - 24048 * q^49 - 1176 * q^51 + 2380 * q^53 + 620 * q^55 + 996 * q^59 + 1500 * q^61 + 2450 * q^63 - 2576 * q^65 - 3060 * q^67 + 440 * q^69 + 1240 * q^71 - 2880 * q^73 + 5268 * q^75 - 624 * q^79 - 11510 * q^81 - 1870 * q^83 - 2566 * q^85 + 6392 * q^89 + 3696 * q^91 - 266 * q^95 + 1860 * q^97 + 3972 * q^99

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

\( S_{4}^{\mathrm{old}}(1900, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)