Space of modular forms of level 495, weight 3, and Character 495.bt

• Label: 495.3.bt
• Level: $495$
• Weight: $3$
• Character orbit: 495.bt
• Rep. character: $\chi_{495}(58,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $2240$
• Sturm bound: $216$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	495.bt (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 495 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(495, [\chi])\).

	Total	New	Old
Modular forms	2368	2368	0
Cusp forms	2240	2240	0
Eisenstein series	128	128	0

Trace form

2240 * q - 6 * q^2 - 10 * q^3 - 6 * q^5 - 24 * q^6 - 6 * q^7 + 8 * q^8 - 64 * q^10 - 28 * q^11 - 76 * q^12 - 6 * q^13 + 20 * q^15 - 1036 * q^16 - 24 * q^17 + 4 * q^18 + 170 * q^20 - 120 * q^21 - 24 * q^22 + 128 * q^23 + 144 * q^26 + 116 * q^27 + 136 * q^28 - 112 * q^30 - 12 * q^31 - 112 * q^32 - 122 * q^33 - 24 * q^35 + 376 * q^36 + 60 * q^37 + 194 * q^38 + 90 * q^40 - 12 * q^41 - 224 * q^42 - 16 * q^43 + 196 * q^45 - 48 * q^46 - 102 * q^47 + 320 * q^48 + 186 * q^50 - 112 * q^51 + 138 * q^52 + 936 * q^53 - 132 * q^55 + 56 * q^56 + 300 * q^57 + 170 * q^58 - 328 * q^60 - 12 * q^61 + 484 * q^62 + 404 * q^63 - 16 * q^65 - 628 * q^66 - 328 * q^67 - 118 * q^68 + 194 * q^70 - 696 * q^71 - 1106 * q^72 - 24 * q^73 - 92 * q^75 - 160 * q^76 + 612 * q^77 - 584 * q^78 - 2256 * q^80 - 1084 * q^81 - 56 * q^82 - 246 * q^83 - 6 * q^85 - 876 * q^86 - 444 * q^87 + 80 * q^88 - 220 * q^90 + 456 * q^91 - 242 * q^92 - 70 * q^93 + 470 * q^95 - 2204 * q^96 - 108 * q^97 + 360 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

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