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

• Label: 1078.2.f
• Level: $1078$
• Weight: $2$
• Character orbit: 1078.f
• Rep. character: $\chi_{1078}(295,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $164$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.f (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(336\)

Dimensions

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

	Total	New	Old
Modular forms	736	164	572
Cusp forms	608	164	444
Eisenstein series	128	0	128

Trace form

164 * q - q^2 - 4 * q^3 - 41 * q^4 + 2 * q^5 + 5 * q^6 - q^8 - 57 * q^9 - 4 * q^10 + 15 * q^11 + 6 * q^12 - 30 * q^15 - 41 * q^16 - 14 * q^17 + 8 * q^18 + 7 * q^19 + 2 * q^20 + 5 * q^22 + 28 * q^23 + 5 * q^24 - 39 * q^25 - 10 * q^26 - 31 * q^27 + 14 * q^29 + 22 * q^30 - 14 * q^31 + 4 * q^32 - 45 * q^33 - 30 * q^34 - 32 * q^36 + 30 * q^37 + 18 * q^38 + 26 * q^39 - 4 * q^40 - 10 * q^41 + 46 * q^43 + 84 * q^45 + 20 * q^46 - 28 * q^47 - 4 * q^48 + 21 * q^50 - 39 * q^51 + 10 * q^52 + 28 * q^53 - 64 * q^54 + 56 * q^55 + 13 * q^57 - 30 * q^58 + 61 * q^59 + 20 * q^60 - 32 * q^61 + 26 * q^62 - 41 * q^64 - 24 * q^66 - 42 * q^67 - 14 * q^68 + 10 * q^69 - 48 * q^71 - 17 * q^72 - 14 * q^73 - 34 * q^74 - 49 * q^75 - 18 * q^76 - 48 * q^78 + 46 * q^79 - 8 * q^80 - 106 * q^81 - 7 * q^82 - 11 * q^83 - 58 * q^85 + q^86 - 52 * q^87 - 5 * q^88 + 46 * q^89 + 16 * q^90 - 22 * q^92 + 70 * q^93 - 44 * q^94 + 10 * q^95 + 33 * q^97 - 21 * 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

\( S_{2}^{\mathrm{old}}(1078, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)