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

• Label: 2300.2.bk
• Level: $2300$
• Weight: $2$
• Character orbit: 2300.bk
• Rep. character: $\chi_{2300}(41,\cdot)$
• Character field: $\Q(\zeta_{55})$
• Dimension: $2400$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2300.bk (of order \(55\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 575 \)
Character field:			\(\Q(\zeta_{55})\)
Sturm bound:			\(720\)

Dimensions

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

	Total	New	Old
Modular forms	14640	2400	12240
Cusp forms	14160	2400	11760
Eisenstein series	480	0	480

Trace form

2400 * q - 4 * q^3 + 6 * q^5 - 4 * q^7 + 56 * q^9 + 10 * q^11 - 8 * q^13 - 23 * q^15 + 6 * q^17 + 16 * q^19 + 8 * q^21 - 60 * q^23 + 64 * q^25 + 26 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^33 + 16 * q^35 - 84 * q^37 - 24 * q^39 - 100 * q^43 - 14 * q^45 + 124 * q^47 - 260 * q^49 - 32 * q^51 + 20 * q^53 - 2 * q^55 - 56 * q^57 - 18 * q^59 + 8 * q^61 - 22 * q^63 + 79 * q^65 + 66 * q^67 - 129 * q^69 + 78 * q^71 - 20 * q^73 - 212 * q^75 + 52 * q^77 + 16 * q^79 + 150 * q^81 + 86 * q^83 + 44 * q^85 - 124 * q^87 + 4 * q^89 - 12 * q^91 - 36 * q^93 + 187 * q^95 + 72 * q^97 + 62 * q^99

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(2300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2300, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 2}\)