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

• Label: 1078.2.r
• Level: $1078$
• Weight: $2$
• Character orbit: 1078.r
• Rep. character: $\chi_{1078}(23,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $576$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.r (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Sturm bound:			\(336\)

Dimensions

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

	Total	New	Old
Modular forms	2064	576	1488
Cusp forms	1968	576	1392
Eisenstein series	96	0	96

Trace form

576 * q + 48 * q^4 - 4 * q^5 + 20 * q^6 + 8 * q^7 + 84 * q^9 - 8 * q^13 + 8 * q^14 - 24 * q^15 + 48 * q^16 + 12 * q^17 + 8 * q^20 - 16 * q^21 + 4 * q^24 + 56 * q^25 - 12 * q^26 + 24 * q^27 - 4 * q^28 + 4 * q^29 + 16 * q^30 - 4 * q^31 - 4 * q^33 + 8 * q^34 - 4 * q^35 - 84 * q^36 - 8 * q^37 - 4 * q^38 - 52 * q^39 - 88 * q^41 + 48 * q^42 + 8 * q^43 + 4 * q^45 - 156 * q^46 + 44 * q^47 - 16 * q^49 - 16 * q^50 + 12 * q^51 + 32 * q^52 - 52 * q^53 - 152 * q^54 - 4 * q^56 + 92 * q^57 - 52 * q^58 - 116 * q^59 + 12 * q^60 + 36 * q^61 - 24 * q^62 + 104 * q^63 - 96 * q^64 + 28 * q^65 - 8 * q^66 + 12 * q^67 + 12 * q^68 - 24 * q^69 - 44 * q^70 + 44 * q^71 - 16 * q^73 + 12 * q^74 + 108 * q^75 - 4 * q^77 + 80 * q^78 - 4 * q^79 + 24 * q^80 + 108 * q^81 - 8 * q^82 + 44 * q^83 + 80 * q^84 + 16 * q^85 + 12 * q^86 + 12 * q^87 + 12 * q^90 - 156 * q^91 - 104 * q^93 - 8 * q^94 + 28 * q^95 + 4 * q^96 - 16 * q^97 + 48 * q^98

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

\( S_{2}^{\mathrm{old}}(1078, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)