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

• Label: 3825.2.da
• Level: $3825$
• Weight: $2$
• Character orbit: 3825.da
• Rep. character: $\chi_{3825}(32,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $2560$
• Sturm bound: $1080$

Defining parameters

Level:	\( N \)	\(=\)	\( 3825 = 3^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3825.da (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 765 \)
Character field:			\(\Q(\zeta_{24})\)
Sturm bound:			\(1080\)

Dimensions

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

	Total	New	Old
Modular forms	4416	2624	1792
Cusp forms	4224	2560	1664
Eisenstein series	192	64	128

Trace form

2560 * q + 8 * q^3 - 1264 * q^4 - 16 * q^6 + 4 * q^7 - 24 * q^11 - 12 * q^12 - 1248 * q^16 + 16 * q^18 - 12 * q^22 + 12 * q^23 - 32 * q^24 + 20 * q^27 - 32 * q^28 - 8 * q^31 + 16 * q^33 - 16 * q^34 + 16 * q^36 + 16 * q^37 - 48 * q^38 - 128 * q^39 - 24 * q^41 + 48 * q^42 + 64 * q^46 - 32 * q^48 - 32 * q^51 - 56 * q^52 + 16 * q^54 - 24 * q^56 + 76 * q^57 - 12 * q^58 - 72 * q^59 - 8 * q^61 - 12 * q^63 + 2400 * q^64 - 16 * q^66 + 8 * q^67 - 36 * q^68 + 152 * q^72 + 16 * q^73 + 48 * q^74 - 40 * q^76 + 24 * q^77 + 152 * q^78 - 48 * q^79 - 96 * q^82 + 24 * q^83 - 48 * q^86 + 12 * q^88 + 64 * q^91 - 240 * q^92 + 32 * q^94 + 64 * q^96 + 52 * q^97 - 24 * q^99

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

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