Space of modular forms of level 756, weight 4, and Character 756.cd

• Label: 756.4.cd
• Level: $756$
• Weight: $4$
• Character orbit: 756.cd
• Rep. character: $\chi_{756}(31,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $2568$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	756.cd (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 756 \)
Character field:			\(\Q(\zeta_{18})\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(756, [\chi])\).

	Total	New	Old
Modular forms	2616	2616	0
Cusp forms	2568	2568	0
Eisenstein series	48	48	0

Trace form

2568 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^10 - 9 * q^12 - 156 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 252 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 108 * q^29 + 159 * q^30 + 1377 * q^32 - 18 * q^33 - 72 * q^34 - 1062 * q^36 - 12 * q^37 - 9 * q^38 - 9 * q^40 + 1179 * q^42 - 6 * q^44 + 1962 * q^45 - 6 * q^46 - 12 * q^49 + 363 * q^50 - 9 * q^52 - 12 * q^53 + 6669 * q^54 - 3009 * q^56 - 186 * q^57 - 3 * q^58 + 3657 * q^60 - 18 * q^61 + 1881 * q^62 - 6 * q^64 + 1386 * q^65 - 9 * q^66 - 7074 * q^68 + 4680 * q^69 + 999 * q^70 + 87 * q^72 + 2631 * q^74 + 576 * q^76 + 972 * q^77 + 150 * q^78 - 18 * q^80 + 906 * q^81 - 18 * q^82 + 633 * q^84 + 726 * q^85 - 4185 * q^86 + 1533 * q^88 - 18 * q^89 - 6561 * q^90 + 7968 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 972 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(756, [\chi])\) into newform subspaces

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