Space of modular forms of level 2400, weight 4, and Character 2400.by

• Label: 2400.4.by
• Level: $2400$
• Weight: $4$
• Character orbit: 2400.by
• Rep. character: $\chi_{2400}(251,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $3624$
• Sturm bound: $1920$

Defining parameters

Level:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2400.by (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 96 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(1920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2400, [\chi])\).

	Total	New	Old
Modular forms	5808	3672	2136
Cusp forms	5712	3624	2088
Eisenstein series	96	48	48

Trace form

3624 * q + 4 * q^3 + 8 * q^4 - 12 * q^6 + 8 * q^7 + 4 * q^9 + 4 * q^12 + 8 * q^13 + 456 * q^16 + 4 * q^18 + 8 * q^19 - 12 * q^21 + 440 * q^22 + 504 * q^24 + 268 * q^27 + 8 * q^28 + 8 * q^33 - 184 * q^34 + 1448 * q^36 + 8 * q^37 - 596 * q^39 + 904 * q^42 + 8 * q^43 - 1464 * q^46 + 2448 * q^48 + 96 * q^51 + 800 * q^52 - 216 * q^54 + 4 * q^57 - 4384 * q^58 - 1848 * q^61 + 3032 * q^64 + 3252 * q^66 - 3256 * q^67 + 4 * q^69 - 1376 * q^72 + 8 * q^73 - 5232 * q^76 - 8380 * q^78 - 5648 * q^79 + 3488 * q^82 - 2408 * q^84 + 1292 * q^87 + 1568 * q^88 - 3624 * q^91 - 104 * q^93 + 5936 * q^94 + 12624 * q^96 + 16 * q^97 + 5316 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(2400, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2400, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2400, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)