Space of modular forms of level 3825, weight 2, and Character 3825.s

• Label: 3825.2.s
• Level: $3825$
• Weight: $2$
• Character orbit: 3825.s
• Rep. character: $\chi_{3825}(557,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $216$
• Sturm bound: $1080$

Defining parameters

Level:	\( N \)	\(=\)	\( 3825 = 3^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3825.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 255 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3825, [\chi])\).

	Total	New	Old
Modular forms	1128	216	912
Cusp forms	1032	216	816
Eisenstein series	96	0	96

Trace form

\( 216 q + 8 q^{13} - 248 q^{16} - 64 q^{31} + 16 q^{34} + 24 q^{43} - 32 q^{46} + 216 q^{49} + 32 q^{52} - 96 q^{61} - 88 q^{73} + 96 q^{79} + 96 q^{88} + 32 q^{91} - 32 q^{94}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3825, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3825, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3825, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(765, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1275, [\chi])\)\(^{\oplus 2}\)