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

• Label: 3330.2.cb
• Level: $3330$
• Weight: $2$
• Character orbit: 3330.cb
• Rep. character: $\chi_{3330}(181,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $372$
• Sturm bound: $1368$

Defining parameters

Level:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.cb (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{9})\)
Sturm bound:			\(1368\)

Dimensions

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

	Total	New	Old
Modular forms	4200	372	3828
Cusp forms	4008	372	3636
Eisenstein series	192	0	192

Trace form

372 * q - 24 * q^7 + 6 * q^10 + 12 * q^13 - 6 * q^14 - 18 * q^19 - 72 * q^23 + 12 * q^28 - 12 * q^29 + 36 * q^34 + 12 * q^35 + 60 * q^37 + 48 * q^38 - 60 * q^41 + 96 * q^43 + 6 * q^44 + 6 * q^46 - 12 * q^47 + 12 * q^49 - 24 * q^52 - 12 * q^55 - 48 * q^61 - 60 * q^62 - 186 * q^64 + 6 * q^65 + 72 * q^67 + 24 * q^68 - 84 * q^71 - 72 * q^73 + 60 * q^74 - 18 * q^76 - 12 * q^77 + 12 * q^79 - 48 * q^82 - 24 * q^83 + 12 * q^85 - 12 * q^86 + 54 * q^89 + 18 * q^91 + 12 * q^92 + 18 * q^94 + 48 * q^95 + 24 * q^97 + 48 * q^98

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

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)