Space of modular forms of level 2205, weight 4, and Character 2205.cn

• Label: 2205.4.cn
• Level: $2205$
• Weight: $4$
• Character orbit: 2205.cn
• Rep. character: $\chi_{2205}(64,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $2508$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2205.cn (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 245 \)
Character field:			\(\Q(\zeta_{14})\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2205, [\chi])\).

	Total	New	Old
Modular forms	6096	2532	3564
Cusp forms	6000	2508	3492
Eisenstein series	96	24	72

Trace form

2508 * q + 1654 * q^4 - 3 * q^5 - 39 * q^10 + 122 * q^11 + 186 * q^14 - 6690 * q^16 + 676 * q^19 - 601 * q^20 - 145 * q^25 - 466 * q^26 - 88 * q^29 - 1936 * q^31 - 94 * q^34 - 265 * q^35 - 491 * q^40 - 1390 * q^41 + 1382 * q^44 + 770 * q^46 + 980 * q^49 + 4718 * q^50 - 2471 * q^55 + 494 * q^56 + 4760 * q^59 + 2358 * q^61 + 25370 * q^64 - 781 * q^65 + 5843 * q^70 - 3938 * q^71 - 98 * q^74 + 3076 * q^76 - 1368 * q^79 + 7032 * q^80 + 445 * q^85 + 4326 * q^86 + 6882 * q^89 - 1216 * q^91 - 3094 * q^94 + 854 * q^95

Decomposition of \(S_{4}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2205, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)