Space of modular forms of level 2116, weight 2, and Character 2116.e

• Label: 2116.2.e
• Level: $2116$
• Weight: $2$
• Character orbit: 2116.e
• Rep. character: $\chi_{2116}(177,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $420$
• Sturm bound: $552$

Defining parameters

Level:	\( N \)	\(=\)	\( 2116 = 2^{2} \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2116.e (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Sturm bound:			\(552\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2116, [\chi])\).

	Total	New	Old
Modular forms	3120	420	2700
Cusp forms	2400	420	1980
Eisenstein series	720	0	720

Trace form

420 * q - 2 * q^3 - 2 * q^5 - 2 * q^7 - 40 * q^9 + 2 * q^11 - 6 * q^13 + 17 * q^15 + 9 * q^17 + 11 * q^19 + 47 * q^21 - 28 * q^25 + 19 * q^27 - q^29 + 11 * q^31 + 5 * q^33 - 16 * q^35 - 34 * q^37 - 30 * q^39 - 30 * q^41 - 44 * q^43 - 78 * q^45 - 66 * q^47 - 106 * q^49 - 62 * q^51 - 14 * q^53 - 22 * q^55 - 3 * q^57 + 8 * q^59 + 56 * q^61 + 27 * q^63 + 87 * q^65 + 44 * q^67 + 39 * q^71 + 20 * q^73 + 45 * q^75 + 39 * q^77 + 6 * q^79 - 42 * q^81 + 25 * q^83 - 2 * q^85 - 56 * q^87 - 10 * q^89 - 26 * q^91 + 14 * q^93 - 33 * q^95 + q^97 + q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2116, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2116, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2116, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(529, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1058, [\chi])\)\(^{\oplus 2}\)