Space of modular forms of level 456, weight 3, and Character 456.s

• Label: 456.3.s
• Level: $456$
• Weight: $3$
• Character orbit: 456.s
• Rep. character: $\chi_{456}(107,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $312$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	456.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 456 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(456, [\chi])\).

	Total	New	Old
Modular forms	328	328	0
Cusp forms	312	312	0
Eisenstein series	16	16	0

Trace form

312 * q - 6 * q^3 - 4 * q^4 + 7 * q^6 - 2 * q^9 + 24 * q^10 + 12 * q^16 - 40 * q^19 + 18 * q^22 - 53 * q^24 - 704 * q^25 + 30 * q^28 + 136 * q^30 + 48 * q^33 + 36 * q^34 - 35 * q^36 + 144 * q^40 - 16 * q^42 - 4 * q^43 + 63 * q^48 - 1896 * q^49 - 6 * q^51 + 114 * q^52 - 16 * q^54 + 18 * q^57 + 40 * q^58 - 174 * q^60 + 704 * q^64 + 31 * q^66 - 12 * q^67 + 720 * q^70 - 237 * q^72 - 84 * q^73 + 620 * q^76 + 402 * q^78 + 54 * q^81 - 54 * q^82 + 330 * q^90 + 576 * q^91 - 442 * q^96 - 12 * q^97 + 32 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(456, [\chi])\) into newform subspaces

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