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

• Label: 1078.2.q
• Level: $1078$
• Weight: $2$
• Character orbit: 1078.q
• Rep. character: $\chi_{1078}(361,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $320$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.q (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{15})\)
Sturm bound:			\(336\)

Dimensions

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

	Total	New	Old
Modular forms	1472	320	1152
Cusp forms	1216	320	896
Eisenstein series	256	0	256

Trace form

320 * q + 40 * q^4 + 4 * q^5 + 8 * q^6 + 64 * q^9 + 20 * q^10 - 4 * q^11 + 8 * q^13 - 36 * q^15 + 40 * q^16 - 2 * q^17 + 8 * q^18 - 8 * q^20 + 8 * q^22 + 16 * q^23 - 4 * q^24 + 72 * q^25 - 8 * q^26 + 36 * q^27 + 44 * q^29 - 16 * q^30 - 6 * q^31 - 46 * q^33 + 32 * q^34 - 48 * q^36 + 4 * q^38 + 28 * q^39 - 10 * q^40 + 56 * q^41 - 40 * q^43 - 14 * q^44 - 4 * q^45 - 12 * q^46 + 44 * q^47 - 32 * q^50 - 4 * q^51 - 4 * q^52 + 16 * q^53 + 64 * q^54 + 20 * q^55 + 40 * q^57 - 20 * q^58 + 4 * q^59 - 12 * q^60 + 34 * q^61 - 16 * q^62 - 80 * q^64 - 80 * q^65 - 32 * q^66 - 80 * q^67 - 2 * q^68 - 176 * q^69 - 40 * q^71 - 12 * q^72 + 6 * q^73 - 8 * q^74 - 20 * q^75 - 40 * q^76 - 160 * q^78 - 34 * q^79 - 6 * q^80 - 60 * q^81 - 12 * q^82 - 80 * q^83 + 36 * q^85 - 34 * q^86 - 112 * q^87 - 14 * q^88 - 20 * q^89 - 88 * q^90 + 28 * q^92 - 50 * q^93 - 52 * q^94 + 106 * q^95 - 4 * q^96 - 36 * q^97 + 152 * 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

\( S_{2}^{\mathrm{old}}(1078, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)