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

• Label: 495.3.be
• Level: $495$
• Weight: $3$
• Character orbit: 495.be
• Rep. character: $\chi_{495}(67,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $480$
• Sturm bound: $216$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	495.be (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(216\)

Dimensions

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

	Total	New	Old
Modular forms	592	480	112
Cusp forms	560	480	80
Eisenstein series	32	0	32

Trace form

480 * q + 2 * q^3 + 32 * q^6 + 16 * q^12 + 20 * q^15 + 960 * q^16 - 72 * q^17 - 120 * q^18 + 48 * q^20 + 16 * q^21 - 132 * q^23 + 6 * q^25 + 260 * q^27 - 232 * q^30 + 120 * q^32 - 44 * q^33 - 720 * q^35 - 384 * q^36 + 84 * q^37 - 504 * q^38 + 48 * q^41 - 752 * q^42 - 92 * q^45 + 240 * q^46 - 36 * q^47 + 520 * q^48 + 720 * q^50 + 224 * q^51 + 240 * q^53 - 132 * q^55 + 288 * q^56 + 548 * q^57 + 1184 * q^60 - 192 * q^61 + 576 * q^62 - 472 * q^63 + 648 * q^65 + 78 * q^67 - 1224 * q^68 + 120 * q^71 + 360 * q^72 - 1468 * q^75 + 312 * q^76 - 1580 * q^78 - 672 * q^80 - 44 * q^81 - 192 * q^82 - 504 * q^83 + 192 * q^85 + 72 * q^86 - 664 * q^87 - 224 * q^90 - 864 * q^92 + 1214 * q^93 + 240 * q^95 + 1456 * q^96 - 486 * q^97 + 3312 * 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.

Decomposition of \(S_{3}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(495, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)