Space of modular forms of level 3300, weight 2, and Character 3300.el

• Label: 3300.2.el
• Level: $3300$
• Weight: $2$
• Character orbit: 3300.el
• Rep. character: $\chi_{3300}(329,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $480$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 3300 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3300.el (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 825 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3300, [\chi])\).

	Total	New	Old
Modular forms	2928	480	2448
Cusp forms	2832	480	2352
Eisenstein series	96	0	96

Trace form

\( 480 q + 2 q^{9} + q^{15} + 4 q^{25} + 24 q^{31} + 25 q^{33} - 125 q^{45} + 440 q^{49} - 26 q^{55} + 10 q^{67} - 19 q^{69} + 97 q^{75} + 42 q^{81} - 16 q^{91} - 20 q^{97} + 4 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3300, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3300, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1650, [\chi])\)\(^{\oplus 2}\)