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

• Label: 456.3.bt
• Level: $456$
• Weight: $3$
• Character orbit: 456.bt
• Rep. character: $\chi_{456}(59,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $936$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	456.bt (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 456 \)
Character field:			\(\Q(\zeta_{18})\)
Sturm bound:			\(240\)

Dimensions

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

	Total	New	Old
Modular forms	984	984	0
Cusp forms	936	936	0
Eisenstein series	48	48	0

Trace form

936 * q - 12 * q^3 - 6 * q^4 - 6 * q^6 - 12 * q^9 - 42 * q^10 - 9 * q^12 - 54 * q^16 - 24 * q^19 - 36 * q^22 + 126 * q^24 - 24 * q^25 - 18 * q^27 - 108 * q^28 + 264 * q^30 - 66 * q^33 - 54 * q^34 - 66 * q^36 - 162 * q^40 - 381 * q^42 - 24 * q^43 - 18 * q^46 + 621 * q^48 + 2760 * q^49 - 12 * q^51 - 132 * q^52 - 225 * q^54 - 12 * q^57 + 48 * q^58 + 246 * q^60 + 456 * q^64 - 444 * q^66 - 24 * q^67 - 198 * q^70 + 228 * q^72 + 216 * q^73 - 588 * q^76 - 447 * q^78 - 180 * q^81 - 1020 * q^82 - 9 * q^84 - 954 * q^88 - 114 * q^90 - 612 * q^91 - 930 * q^96 - 24 * q^97 - 498 * 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.