Space of modular forms of level 2320, weight 4, and Character 2320.em

• Label: 2320.4.em
• Level: $2320$
• Weight: $4$
• Character orbit: 2320.em
• Rep. character: $\chi_{2320}(37,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $12912$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 2320 = 2^{4} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2320.em (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2320 \)
Character field:			\(\Q(\zeta_{28})\)
Sturm bound:			\(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2320, [\chi])\).

	Total	New	Old
Modular forms	13008	13008	0
Cusp forms	12912	12912	0
Eisenstein series	96	96	0

Trace form

12912 * q - 14 * q^2 + 4 * q^3 - 14 * q^5 - 28 * q^6 - 14 * q^8 + 4 * q^10 - 28 * q^11 - 24 * q^12 + 32 * q^14 - 24 * q^15 - 20 * q^16 + 1284 * q^18 - 10 * q^20 - 28 * q^21 - 46 * q^22 - 24 * q^26 - 104 * q^27 + 648 * q^30 - 48 * q^31 - 14 * q^32 - 28 * q^33 + 160 * q^34 - 14 * q^35 - 532 * q^36 + 4 * q^37 - 3056 * q^38 + 216 * q^39 + 316 * q^40 - 154 * q^42 - 24 * q^43 + 1032 * q^44 - 510 * q^45 - 912 * q^46 - 20 * q^47 - 2650 * q^48 + 802 * q^50 - 28 * q^51 + 5664 * q^52 - 20 * q^53 - 500 * q^55 - 192 * q^56 - 216 * q^57 + 6850 * q^58 - 1156 * q^60 - 20 * q^61 - 1216 * q^62 - 28 * q^63 - 3024 * q^64 - 20 * q^65 + 480 * q^66 - 28 * q^67 + 6076 * q^68 - 216 * q^69 - 9662 * q^70 - 122 * q^72 - 1480 * q^73 + 2336 * q^74 - 108 * q^75 + 144 * q^76 - 1396 * q^77 + 998 * q^78 - 1490 * q^80 + 169088 * q^81 - 1358 * q^82 + 10644 * q^84 + 1740 * q^85 - 9528 * q^86 - 108 * q^87 - 1608 * q^88 + 44 * q^90 - 28 * q^91 - 874 * q^92 + 216 * q^93 + 1296 * q^94 - 24 * q^95 - 28 * q^96 - 20 * q^97 + 1330 * q^98 + 216 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(2320, [\chi])\) into newform subspaces

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