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

• Label: 2205.2.bt
• Level: $2205$
• Weight: $2$
• Character orbit: 2205.bt
• Rep. character: $\chi_{2205}(178,\cdot)$
• 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.bt (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 + 4 * q^2 + 6 * q^3 + 6 * q^5 - 40 * q^8 + 12 * q^10 + 4 * q^11 + 18 * q^12 - 22 * q^15 - 824 * q^16 + 30 * q^17 + 18 * q^18 - 48 * q^20 + 14 * q^23 - 2 * q^25 + 24 * q^26 + 36 * q^27 - 6 * q^30 + 4 * q^32 + 6 * q^33 - 104 * q^36 + 4 * q^37 + 6 * q^38 + 6 * q^40 - 12 * q^41 - 8 * q^43 + 54 * q^45 + 20 * q^46 - 18 * q^48 + 56 * q^50 - 68 * q^51 - 42 * q^52 - 16 * q^53 - 8 * q^57 - 22 * q^58 - 154 * q^60 + 100 * q^65 + 12 * q^66 + 4 * q^67 - 90 * q^68 - 74 * q^72 + 12 * q^73 + 54 * q^75 - 48 * q^76 - 50 * q^78 - 12 * q^80 + 68 * q^81 + 24 * q^82 + 84 * q^83 - 8 * q^85 + 40 * q^86 - 12 * q^87 - 18 * q^88 - 36 * q^90 + 20 * q^92 + 30 * q^93 + 20 * q^95 + 168 * q^96

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

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