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

• Label: 2300.2.m
• Level: $2300$
• Weight: $2$
• Character orbit: 2300.m
• Rep. character: $\chi_{2300}(461,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $216$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2300.m (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(720\)

Dimensions

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

	Total	New	Old
Modular forms	1464	216	1248
Cusp forms	1416	216	1200
Eisenstein series	48	0	48

Trace form

216 * q + 2 * q^5 + 8 * q^7 - 50 * q^9 + 12 * q^13 - 2 * q^15 - 8 * q^17 - 12 * q^21 + 10 * q^25 + 42 * q^27 + 24 * q^29 - 12 * q^31 + 62 * q^33 - 10 * q^35 - 30 * q^37 - 20 * q^39 + 46 * q^41 - 128 * q^45 + 6 * q^47 + 192 * q^49 + 4 * q^51 - 62 * q^53 + 14 * q^55 - 176 * q^57 + 44 * q^61 + 86 * q^63 + 34 * q^65 + 8 * q^67 + 8 * q^69 - 10 * q^71 - 16 * q^73 + 28 * q^75 + 68 * q^77 + 32 * q^79 - 54 * q^81 + 6 * q^83 - 12 * q^85 + 10 * q^87 - 12 * q^91 - 8 * q^93 - 12 * q^95 + 8 * q^97 - 32 * 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

\( S_{2}^{\mathrm{old}}(2300, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 2}\)