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

• Label: 1900.2.ce
• Level: $1900$
• Weight: $2$
• Character orbit: 1900.ce
• Rep. character: $\chi_{1900}(61,\cdot)$
• Character field: $\Q(\zeta_{45})$
• Dimension: $1200$
• Sturm bound: $600$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.ce (of order \(45\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 475 \)
Character field:			\(\Q(\zeta_{45})\)
Sturm bound:			\(600\)

Dimensions

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

	Total	New	Old
Modular forms	7344	1200	6144
Cusp forms	7056	1200	5856
Eisenstein series	288	0	288

Trace form

1200 * q - 6 * q^7 + 9 * q^11 - 45 * q^15 - 18 * q^17 + 42 * q^23 - 42 * q^25 + 18 * q^29 - 54 * q^33 - 39 * q^35 + 180 * q^43 + 66 * q^45 - 36 * q^47 - 630 * q^49 + 60 * q^51 - 18 * q^53 + 72 * q^55 - 198 * q^57 - 36 * q^59 - 72 * q^61 + 36 * q^63 - 60 * q^65 - 72 * q^67 + 48 * q^69 - 114 * q^71 - 18 * q^73 - 12 * q^77 + 24 * q^79 - 48 * q^81 + 102 * q^85 + 84 * q^87 + 36 * q^89 + 204 * q^93 - 9 * q^95 - 78 * q^97 + 96 * 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

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