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

• Label: 600.3.n
• Level: $600$
• Weight: $3$
• Character orbit: 600.n
• Rep. character: $\chi_{600}(101,\cdot)$
• Character field: $\Q$
• Dimension: $146$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	600.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Sturm bound:			\(360\)

Dimensions

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

	Total	New	Old
Modular forms	252	158	94
Cusp forms	228	146	82
Eisenstein series	24	12	12

Trace form

146 * q + 4 * q^4 - 2 * q^6 + 4 * q^7 + 2 * q^9 + 12 * q^12 - 32 * q^16 + 36 * q^18 + 28 * q^22 - 18 * q^24 - 44 * q^28 - 76 * q^31 + 28 * q^33 + 60 * q^34 - 114 * q^36 + 152 * q^39 + 96 * q^42 - 40 * q^46 - 4 * q^48 + 790 * q^49 - 136 * q^52 + 144 * q^54 + 24 * q^57 + 68 * q^58 - 60 * q^63 - 176 * q^64 - 70 * q^66 - 288 * q^72 + 84 * q^73 - 20 * q^76 + 152 * q^78 + 132 * q^79 + 66 * q^81 - 296 * q^82 - 532 * q^84 - 12 * q^87 - 140 * q^88 - 432 * q^94 - 194 * q^96 + 132 * 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.

Decomposition of \(S_{3}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(600, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)