Space of modular forms of level 1078, weight 2, and Character 1078.bc

• Label: 1078.2.bc
• Level: $1078$
• Weight: $2$
• Character orbit: 1078.bc
• Rep. character: $\chi_{1078}(9,\cdot)$
• Character field: $\Q(\zeta_{105})$
• Dimension: $2688$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.bc (of order \(105\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 539 \)
Character field:			\(\Q(\zeta_{105})\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1078, [\chi])\).

	Total	New	Old
Modular forms	8256	2688	5568
Cusp forms	7872	2688	5184
Eisenstein series	384	0	384

Trace form

2688 * q - 56 * q^4 + 4 * q^5 + 8 * q^6 + 2 * q^7 - 56 * q^9 + 20 * q^10 + 18 * q^11 + 8 * q^13 + 2 * q^14 - 30 * q^15 - 56 * q^16 - 44 * q^17 + 8 * q^18 + 28 * q^19 + 20 * q^20 + 16 * q^21 + 6 * q^22 + 100 * q^23 - 4 * q^24 - 48 * q^25 + 20 * q^26 - 90 * q^27 + 14 * q^28 + 12 * q^29 - 6 * q^31 - 46 * q^33 + 32 * q^34 + 62 * q^35 + 112 * q^36 + 16 * q^37 - 52 * q^38 + 20 * q^39 + 74 * q^40 + 56 * q^41 + 66 * q^42 - 40 * q^43 - 34 * q^44 - 32 * q^45 + 4 * q^46 - 138 * q^47 - 178 * q^49 - 32 * q^50 + 324 * q^51 - 4 * q^52 + 100 * q^53 + 64 * q^54 - 22 * q^55 - 52 * q^56 + 8 * q^57 - 244 * q^58 + 32 * q^59 - 52 * q^60 + 34 * q^61 + 68 * q^62 + 10 * q^63 + 112 * q^64 - 32 * q^65 - 32 * q^66 - 48 * q^67 + 54 * q^68 - 120 * q^69 - 48 * q^70 + 24 * q^71 - 12 * q^72 - 120 * q^73 + 20 * q^74 - 20 * q^75 - 40 * q^76 + 36 * q^77 - 32 * q^78 + 14 * q^79 - 6 * q^80 + 52 * q^81 - 12 * q^82 + 4 * q^83 - 36 * q^84 + 52 * q^85 - 144 * q^86 - 308 * q^87 - 62 * q^88 + 92 * q^89 - 88 * q^90 + 134 * q^91 + 28 * q^92 + 6 * q^93 - 262 * q^94 - 182 * q^95 - 4 * q^96 - 288 * q^97 + 8 * q^98 - 840 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1078, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1078, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1078, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)