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

• Label: 1900.4.o
• Level: $1900$
• Weight: $4$
• Character orbit: 1900.o
• Rep. character: $\chi_{1900}(1551,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $1128$
• Sturm bound: $1200$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1900.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(1200\)

Dimensions

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

	Total	New	Old
Modular forms	1824	1152	672
Cusp forms	1776	1128	648
Eisenstein series	48	24	24

Trace form

1128 * q + 3 * q^2 - 5 * q^4 - 25 * q^6 - 4976 * q^9 + 114 * q^13 + 174 * q^14 + 63 * q^16 + 78 * q^17 - 360 * q^21 - 21 * q^22 - 29 * q^24 - 8 * q^26 - 32 * q^28 + 6 * q^29 - 357 * q^32 + 246 * q^33 + 420 * q^34 - 262 * q^36 + 1556 * q^38 - 312 * q^41 - 874 * q^42 + 377 * q^44 - 1707 * q^48 - 52920 * q^49 - 1080 * q^52 - 582 * q^53 - 271 * q^54 - 374 * q^57 - 3224 * q^58 - 1390 * q^61 + 632 * q^62 + 778 * q^64 + 2129 * q^66 - 376 * q^68 - 1386 * q^72 - 88 * q^73 - 3326 * q^74 + 3579 * q^76 - 800 * q^77 - 654 * q^78 - 43472 * q^81 - 1609 * q^82 - 3072 * q^86 - 2298 * q^89 - 1648 * q^92 + 68 * q^93 - 6734 * q^96 - 780 * q^97 + 1815 * 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

\( S_{4}^{\mathrm{old}}(1900, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)