Space of modular forms of level 1156, weight 2, and Character 1156.k

• Label: 1156.2.k
• Level: $1156$
• Weight: $2$
• Character orbit: 1156.k
• Rep. character: $\chi_{1156}(69,\cdot)$
• Character field: $\Q(\zeta_{17})$
• Dimension: $416$
• Sturm bound: $306$

Defining parameters

Level:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1156.k (of order \(17\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 289 \)
Character field:			\(\Q(\zeta_{17})\)
Sturm bound:			\(306\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1156, [\chi])\).

	Total	New	Old
Modular forms	2496	416	2080
Cusp forms	2400	416	1984
Eisenstein series	96	0	96

Trace form

416 * q - 2 * q^3 + 17 * q^5 + 2 * q^7 - 26 * q^9 + 6 * q^11 - 6 * q^13 + 10 * q^15 + 2 * q^17 - 6 * q^19 - 39 * q^21 + 6 * q^23 + 11 * q^25 + 43 * q^27 + 2 * q^31 - 49 * q^33 - 8 * q^35 - 16 * q^37 - 84 * q^39 + 12 * q^41 - 2 * q^43 - 129 * q^45 - 19 * q^47 - 20 * q^49 + 70 * q^51 - 27 * q^53 + 14 * q^55 + 8 * q^57 - 10 * q^59 + 8 * q^61 - 71 * q^63 + 24 * q^65 + 105 * q^67 - 117 * q^69 + 6 * q^71 - 4 * q^73 - 150 * q^75 + 36 * q^77 + 31 * q^79 + 110 * q^81 + 46 * q^83 - 51 * q^85 - 12 * q^87 - 10 * q^89 - 52 * q^91 - 16 * q^93 - 24 * q^95 - 4 * q^97 - 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1156, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1156, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(578, [\chi])\)\(^{\oplus 2}\)