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

• Label: 2205.4.cs
• Level: $2205$
• Weight: $4$
• Character orbit: 2205.cs
• Rep. character: $\chi_{2205}(46,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $3360$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2205.cs (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	12192	3360	8832
Cusp forms	12000	3360	8640
Eisenstein series	192	0	192

Trace form

3360 * q + 1120 * q^4 + 10 * q^5 - 20 * q^7 - 20 * q^10 + 14 * q^11 + 352 * q^13 - 144 * q^14 + 4508 * q^16 + 140 * q^17 + 154 * q^19 - 200 * q^20 + 616 * q^22 - 672 * q^23 + 7000 * q^25 - 94 * q^26 - 246 * q^28 + 378 * q^29 + 160 * q^31 + 560 * q^32 + 260 * q^34 - 800 * q^35 + 3808 * q^37 + 3320 * q^38 - 240 * q^40 - 1176 * q^41 - 280 * q^43 - 5418 * q^44 - 3822 * q^46 - 2508 * q^47 + 3078 * q^49 + 6940 * q^52 - 140 * q^53 + 1120 * q^55 + 3296 * q^56 - 3682 * q^58 + 6 * q^59 + 7462 * q^61 + 1504 * q^62 - 35728 * q^64 - 210 * q^65 + 252 * q^67 - 9716 * q^68 - 520 * q^70 + 952 * q^71 + 2676 * q^73 - 1414 * q^74 - 4916 * q^76 + 3232 * q^77 - 700 * q^79 - 6880 * q^80 + 14534 * q^82 - 5132 * q^83 + 560 * q^85 + 4018 * q^86 - 10010 * q^88 - 826 * q^89 - 14826 * q^91 + 14588 * q^92 - 21074 * q^94 + 280 * q^95 - 4288 * q^97 + 17142 * q^98

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

\( S_{4}^{\mathrm{old}}(2205, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)