Space of modular forms of level 300, weight 4, and Character 300.n

• Label: 300.4.n
• Level: $300$
• Weight: $4$
• Character orbit: 300.n
• Rep. character: $\chi_{300}(11,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $704$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	300.n (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 300 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(300, [\chi])\).

	Total	New	Old
Modular forms	736	736	0
Cusp forms	704	704	0
Eisenstein series	32	32	0

Trace form

704 * q - 6 * q^4 + 13 * q^6 - 6 * q^9 - 60 * q^10 - 57 * q^12 - 12 * q^13 - 114 * q^16 + 214 * q^18 + 156 * q^21 - 190 * q^22 + 32 * q^24 - 100 * q^25 + 810 * q^28 + 275 * q^30 + 102 * q^33 + 106 * q^34 - 205 * q^36 - 804 * q^37 - 120 * q^40 + 473 * q^42 - 750 * q^45 + 446 * q^46 + 2798 * q^48 - 30232 * q^49 - 596 * q^52 + 1144 * q^54 + 724 * q^57 + 3022 * q^58 - 6400 * q^60 + 612 * q^61 - 942 * q^64 + 2204 * q^66 - 642 * q^69 + 2400 * q^70 + 1603 * q^72 - 996 * q^73 - 2720 * q^76 + 4967 * q^78 - 462 * q^81 + 9900 * q^82 + 3342 * q^84 - 3420 * q^85 + 8102 * q^88 + 2030 * q^90 - 2596 * q^93 - 6700 * q^94 + 2614 * q^96 + 5568 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(300, [\chi])\) into newform subspaces

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