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

• Label: 495.3.bn
• Level: $495$
• Weight: $3$
• Character orbit: 495.bn
• Rep. character: $\chi_{495}(86,\cdot)$
• 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.bn (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 - 24 * q^6 - 12 * q^9 + 18 * q^11 - 96 * q^12 + 30 * q^15 + 384 * q^16 - 128 * q^18 - 72 * q^19 - 88 * q^21 + 24 * q^22 + 108 * q^23 + 160 * q^24 - 480 * q^25 - 14 * q^27 + 162 * q^29 + 160 * q^30 - 362 * q^33 - 96 * q^34 - 408 * q^36 - 324 * q^38 + 22 * q^39 - 504 * q^41 - 406 * q^42 + 120 * q^43 - 744 * q^48 + 672 * q^49 + 608 * q^51 + 972 * q^54 - 252 * q^56 - 336 * q^57 + 288 * q^59 + 370 * q^60 - 238 * q^63 + 1536 * q^64 + 180 * q^65 - 118 * q^66 - 168 * q^67 + 306 * q^68 + 672 * q^69 - 840 * q^72 + 144 * q^73 + 288 * q^74 - 60 * q^75 + 144 * q^76 - 702 * q^77 - 2280 * q^78 + 12 * q^79 - 660 * q^81 + 576 * q^82 - 810 * q^83 - 1644 * q^84 - 60 * q^85 - 504 * q^86 - 1228 * q^87 - 144 * q^88 - 320 * q^90 + 252 * q^91 - 396 * q^92 + 358 * q^93 - 762 * q^96 - 540 * q^97 + 904 * 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

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