Space of modular forms of level 2300, weight 2, and Character 2300.bt

• Label: 2300.2.bt
• Level: $2300$
• Weight: $2$
• Character orbit: 2300.bt
• Rep. character: $\chi_{2300}(3,\cdot)$
• Character field: $\Q(\zeta_{220})$
• Dimension: $28480$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2300.bt (of order \(220\) and degree \(80\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2300 \)
Character field:			\(\Q(\zeta_{220})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2300, [\chi])\).

	Total	New	Old
Modular forms	29120	29120	0
Cusp forms	28480	28480	0
Eisenstein series	640	640	0

Trace form

28480 * q - 72 * q^2 - 90 * q^4 - 144 * q^5 - 54 * q^6 - 72 * q^8 - 180 * q^9 - 72 * q^10 - 84 * q^12 - 144 * q^13 - 90 * q^14 - 54 * q^16 - 144 * q^17 - 52 * q^18 - 76 * q^20 - 108 * q^21 - 172 * q^22 - 144 * q^25 - 144 * q^26 - 56 * q^28 - 180 * q^29 - 92 * q^30 - 92 * q^32 - 120 * q^33 - 90 * q^34 - 22 * q^36 - 144 * q^37 - 80 * q^38 - 192 * q^40 - 108 * q^41 + 112 * q^42 - 90 * q^44 - 280 * q^45 - 60 * q^46 - 300 * q^48 - 236 * q^50 - 20 * q^52 - 96 * q^53 - 350 * q^54 - 54 * q^56 - 136 * q^57 - 32 * q^58 - 48 * q^60 - 108 * q^61 - 108 * q^62 - 90 * q^64 - 112 * q^65 - 6 * q^66 - 196 * q^68 - 200 * q^69 - 216 * q^70 - 256 * q^72 - 144 * q^73 - 176 * q^76 - 136 * q^77 - 100 * q^78 - 294 * q^80 - 756 * q^81 - 80 * q^82 + 70 * q^84 + 72 * q^85 - 54 * q^86 - 40 * q^88 - 180 * q^89 - 354 * q^90 + 22 * q^92 - 472 * q^93 - 90 * q^94 - 94 * q^96 - 144 * q^97 - 20 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2300, [\chi])\) into newform subspaces

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