Space of modular forms of level 1058, weight 2, and Character 1058.c

• Label: 1058.2.c
• Level: $1058$
• Weight: $2$
• Character orbit: 1058.c
• Rep. character: $\chi_{1058}(177,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $420$
• Sturm bound: $276$

Defining parameters

Level:	\( N \)	\(=\)	\( 1058 = 2 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1058.c (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Sturm bound:			\(276\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1058, [\chi])\).

	Total	New	Old
Modular forms	1620	420	1200
Cusp forms	1140	420	720
Eisenstein series	480	0	480

Trace form

420 * q + 4 * q^3 - 42 * q^4 + 10 * q^5 + 4 * q^6 + 4 * q^7 - 34 * q^9 + 2 * q^10 + 14 * q^11 + 4 * q^12 + 12 * q^13 + 12 * q^14 + 2 * q^15 - 42 * q^16 - 6 * q^17 - 28 * q^18 - 4 * q^19 - 12 * q^20 - 34 * q^21 - 12 * q^22 + 4 * q^24 - 46 * q^25 - 6 * q^26 - 26 * q^27 - 18 * q^28 + 14 * q^29 - 20 * q^30 + 14 * q^31 + 26 * q^33 + 20 * q^34 + 14 * q^35 - 34 * q^36 - 10 * q^37 + 22 * q^38 + 12 * q^39 + 2 * q^40 + 30 * q^41 + 32 * q^42 + 10 * q^43 + 14 * q^44 - 36 * q^47 + 4 * q^48 - 40 * q^49 + 24 * q^50 + 28 * q^51 + 12 * q^52 + 28 * q^53 + 18 * q^54 - 4 * q^55 - 10 * q^56 - 30 * q^57 - 16 * q^58 - 34 * q^59 + 2 * q^60 - 34 * q^61 - 30 * q^62 + 6 * q^63 - 42 * q^64 - 78 * q^65 - 40 * q^66 + 14 * q^67 - 28 * q^68 - 104 * q^70 - 30 * q^71 - 28 * q^72 + 44 * q^73 - 46 * q^74 - 36 * q^75 + 18 * q^76 - 6 * q^77 - 2 * q^78 - 42 * q^79 - 12 * q^80 - 30 * q^81 - 4 * q^82 + 10 * q^83 + 10 * q^84 + 46 * q^85 + 12 * q^86 + 70 * q^87 + 10 * q^88 + 62 * q^89 + 90 * q^90 + 76 * q^91 + 128 * q^93 + 56 * q^94 + 66 * q^95 + 4 * q^96 + 16 * q^97 + 4 * q^98 - 26 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1058, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1058, [\chi])\) into lower level spaces

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