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

• Label: 495.3.bm
• Level: $495$
• Weight: $3$
• Character orbit: 495.bm
• Rep. character: $\chi_{495}(61,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $768$
• Sturm bound: $216$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	495.bm (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(216\)

Dimensions

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

	Total	New	Old
Modular forms	1184	768	416
Cusp forms	1120	768	352
Eisenstein series	64	0	64

Trace form

768 * q + 8 * q^3 - 192 * q^4 + 40 * q^6 - 36 * q^9 + 6 * q^11 + 96 * q^12 - 30 * q^15 + 384 * q^16 + 160 * q^18 + 120 * q^19 - 24 * q^22 - 36 * q^23 + 240 * q^24 + 480 * q^25 + 192 * q^26 + 146 * q^27 - 90 * q^29 + 346 * q^33 + 96 * q^34 + 72 * q^36 + 12 * q^38 - 530 * q^39 - 540 * q^41 - 274 * q^42 - 828 * q^44 - 216 * q^47 + 1024 * q^48 - 672 * q^49 - 180 * q^51 + 576 * q^53 + 1356 * q^56 + 840 * q^57 + 24 * q^59 + 50 * q^60 + 550 * q^63 + 1536 * q^64 - 346 * q^66 - 168 * q^67 + 390 * q^68 - 552 * q^69 - 192 * q^71 + 480 * q^72 - 1260 * q^74 - 60 * q^75 + 234 * q^77 - 1768 * q^78 - 720 * q^80 - 1300 * q^81 + 576 * q^82 - 810 * q^83 - 2080 * q^84 + 768 * q^86 + 144 * q^88 - 744 * q^89 + 252 * q^91 - 132 * q^92 - 958 * q^93 + 590 * q^96 + 540 * q^97 + 712 * q^99

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

\( S_{3}^{\mathrm{old}}(495, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)