Space of modular forms of level 2205, weight 2, and Character 2205.by

• Label: 2205.2.by
• Level: $2205$
• Weight: $2$
• Character orbit: 2205.by
• Rep. character: $\chi_{2205}(128,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $928$
• Sturm bound: $672$

Defining parameters

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2205.by (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2205, [\chi])\).

	Total	New	Old
Modular forms	1408	992	416
Cusp forms	1280	928	352
Eisenstein series	128	64	64

Trace form

928 * q + 6 * q^2 + 2 * q^3 + 24 * q^6 + 4 * q^10 + 22 * q^12 + 4 * q^13 - 10 * q^15 + 412 * q^16 + 18 * q^17 + 50 * q^18 + 12 * q^20 - 16 * q^22 + 4 * q^25 + 32 * q^27 + 60 * q^30 - 4 * q^31 + 150 * q^32 - 32 * q^33 - 40 * q^36 + 4 * q^37 + 36 * q^40 + 36 * q^41 - 8 * q^43 + 68 * q^45 - 4 * q^46 + 6 * q^47 - 38 * q^48 - 72 * q^50 - 44 * q^51 + 52 * q^52 - 4 * q^55 - 80 * q^57 + 12 * q^58 + 118 * q^60 + 8 * q^61 + 150 * q^65 + 92 * q^66 - 2 * q^67 + 2 * q^72 + 4 * q^73 - 54 * q^75 + 24 * q^76 - 22 * q^78 - 36 * q^80 - 16 * q^81 + 8 * q^82 + 12 * q^83 - 8 * q^85 + 28 * q^87 + 36 * q^88 + 24 * q^90 - 180 * q^92 - 114 * q^95 + 4 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)