Space of modular forms of level 600, weight 4, and Character 600.v

• Label: 600.4.v
• Level: $600$
• Weight: $4$
• Character orbit: 600.v
• Rep. character: $\chi_{600}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $216$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	600.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(600, [\chi])\).

	Total	New	Old
Modular forms	744	216	528
Cusp forms	696	216	480
Eisenstein series	48	0	48

Trace form

216 * q - 24 * q^6 - 84 * q^8 - 24 * q^12 + 40 * q^16 + 104 * q^17 - 44 * q^22 + 736 * q^26 + 1068 * q^28 - 340 * q^32 + 216 * q^36 + 40 * q^38 + 660 * q^42 - 864 * q^43 + 72 * q^46 - 528 * q^48 + 2976 * q^51 - 2544 * q^52 - 3448 * q^56 - 1004 * q^58 - 2608 * q^62 - 2736 * q^66 - 3696 * q^67 + 1464 * q^68 + 756 * q^72 - 1480 * q^73 + 8032 * q^76 + 72 * q^78 - 17496 * q^81 + 6712 * q^82 + 5360 * q^83 + 6872 * q^86 + 404 * q^88 - 6784 * q^91 - 8432 * q^92 + 2784 * q^96 + 328 * q^97 - 7576 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(600, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)