Space of modular forms of level 1900, weight 2, and Character 1900.z

• Label: 1900.2.z
• Level: $1900$
• Weight: $2$
• Character orbit: 1900.z
• Rep. character: $\chi_{1900}(229,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $184$
• Sturm bound: $600$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.z (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

	Total	New	Old
Modular forms	1224	184	1040
Cusp forms	1176	184	992
Eisenstein series	48	0	48

Trace form

184 * q - 9 * q^5 + 46 * q^9 - 7 * q^11 + 10 * q^15 + 5 * q^17 + 2 * q^19 + 10 * q^23 + 15 * q^25 + 30 * q^27 - 8 * q^29 + 24 * q^31 - 50 * q^33 + 18 * q^35 + 20 * q^37 - 20 * q^39 - 10 * q^41 + 7 * q^45 - 218 * q^49 - 24 * q^51 - 40 * q^53 - 21 * q^55 + 6 * q^59 - 10 * q^61 + 25 * q^63 + 12 * q^65 - 30 * q^67 + 20 * q^69 - 20 * q^71 + 40 * q^73 - 24 * q^75 + 56 * q^79 - 100 * q^81 + 60 * q^83 + 10 * q^85 + 62 * q^89 - 56 * q^91 - q^95 - 20 * q^97 + 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

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