Space of modular forms of level 3330, weight 2, and Character 3330.bw

• Label: 3330.2.bw
• Level: $3330$
• Weight: $2$
• Character orbit: 3330.bw
• Rep. character: $\chi_{3330}(1009,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $188$
• Sturm bound: $1368$

Defining parameters

Level:	$N$	$=$	$3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3330.bw (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$185$
Character field:			$\Q(\zeta_{6})$
Sturm bound:			$1368$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3330, [\chi])$.

	Total	New	Old
Modular forms	1400	188	1212
Cusp forms	1336	188	1148
Eisenstein series	64	0	64

Trace form

188 * q + 94 * q^4 - 4 * q^5 + 4 * q^11 - 8 * q^14 - 94 * q^16 - 18 * q^19 + 4 * q^20 - 16 * q^25 + 36 * q^26 + 16 * q^29 - 32 * q^31 - 8 * q^34 - 4 * q^35 - 44 * q^41 + 2 * q^44 + 26 * q^46 + 102 * q^49 - 28 * q^55 - 4 * q^56 + 6 * q^59 + 28 * q^61 - 188 * q^64 - 30 * q^65 + 4 * q^70 - 4 * q^71 + 30 * q^74 + 18 * q^76 - 20 * q^79 + 8 * q^80 + 4 * q^85 - 12 * q^86 + 10 * q^89 - 8 * q^91 + 10 * q^94 + 4 * q^95

Decomposition of $S_{2}^{\mathrm{new}}(3330, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(3330, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(3330, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(185, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(370, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(555, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(1110, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(1665, [\chi])$$^{\oplus 2}$