Space of modular forms of level 600, weight 3, and Character 600.bj

• Label: 600.3.bj
• Level: $600$
• Weight: $3$
• Character orbit: 600.bj
• Rep. character: $\chi_{600}(221,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $944$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	600.bj (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 600 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(600, [\chi])\).

	Total	New	Old
Modular forms	976	976	0
Cusp forms	944	944	0
Eisenstein series	32	32	0

Trace form

944 * q - 6 * q^4 + 5 * q^6 - 32 * q^7 - 6 * q^9 + 4 * q^10 - 21 * q^12 + 10 * q^15 + 54 * q^16 - 30 * q^18 - 46 * q^22 + 80 * q^24 - 16 * q^25 - 86 * q^28 + 67 * q^30 - 12 * q^31 + 30 * q^33 + 58 * q^34 + 179 * q^36 - 42 * q^39 - 68 * q^40 + 125 * q^42 - 122 * q^46 + 94 * q^48 + 5904 * q^49 - 384 * q^52 - 190 * q^54 + 212 * q^55 - 52 * q^57 + 150 * q^58 + 16 * q^60 - 300 * q^63 - 126 * q^64 + 268 * q^66 - 456 * q^70 - 181 * q^72 - 12 * q^73 + 160 * q^76 - 501 * q^78 - 12 * q^79 - 6 * q^81 + 588 * q^82 - 390 * q^84 - 418 * q^87 + 590 * q^88 - 48 * q^90 + 388 * q^94 + 160 * q^96 - 60 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

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