Space of modular forms of level 495, weight 6, and Character 495.bc

• Label: 495.6.bc
• Level: $495$
• Weight: $6$
• Character orbit: 495.bc
• Rep. character: $\chi_{495}(23,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1200$
• Sturm bound: $432$

Defining parameters

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	495.bc (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(495, [\chi])\).

	Total	New	Old
Modular forms	1456	1200	256
Cusp forms	1424	1200	224
Eisenstein series	32	0	32

Trace form

1200 * q + 2 * q^3 + 320 * q^6 - 128 * q^12 - 4084 * q^15 + 153600 * q^16 - 10632 * q^18 + 11136 * q^20 + 880 * q^21 + 31632 * q^23 - 3306 * q^25 - 14428 * q^27 - 18808 * q^30 - 28920 * q^32 + 15004 * q^33 - 72960 * q^36 + 20028 * q^37 - 81480 * q^41 + 107824 * q^42 + 79612 * q^45 + 31920 * q^46 - 2124 * q^47 + 136024 * q^48 - 79840 * q^51 + 27588 * q^55 - 23040 * q^56 - 108604 * q^57 + 276080 * q^60 + 93480 * q^61 - 183928 * q^63 + 215856 * q^65 + 5514 * q^67 + 205056 * q^68 + 303768 * q^72 - 505972 * q^75 + 100680 * q^76 - 719492 * q^78 + 277660 * q^81 - 552576 * q^82 - 163248 * q^85 + 1113480 * q^86 + 212744 * q^87 + 53056 * q^90 + 1518336 * q^92 + 947726 * q^93 + 7320 * q^95 - 72560 * q^96 + 192726 * q^97

Decomposition of \(S_{6}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(495, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)