Space of modular forms of level 3060, weight 2, and Character 3060.ex

• Label: 3060.2.ex
• Level: $3060$
• Weight: $2$
• Character orbit: 3060.ex
• Rep. character: $\chi_{3060}(491,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $3456$
• Sturm bound: $1296$

Defining parameters

Level:	\( N \)	\(=\)	\( 3060 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3060.ex (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 612 \)
Character field:			\(\Q(\zeta_{24})\)
Sturm bound:			\(1296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3060, [\chi])\).

	Total	New	Old
Modular forms	5248	3456	1792
Cusp forms	5120	3456	1664
Eisenstein series	128	0	128

Trace form

\( 3456 q - 16 q^{9} + 80 q^{24} - 24 q^{34} + 80 q^{42} + 48 q^{46} + 40 q^{54} - 112 q^{57} + 104 q^{66} + 128 q^{69} - 336 q^{74} + 80 q^{84} - 208 q^{96} + 48 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3060, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3060, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3060, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 2}\)