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Properties

Label 1078.2.l
Level $1078$
Weight $2$
Character orbit 1078.l
Rep. character $\chi_{1078}(195,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $160$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 736 160 576
Cusp forms 608 160 448
Eisenstein series 128 0 128

Trace form

\( 160 q + 40 q^{4} + 64 q^{9} + O(q^{10}) \) \( 160 q + 40 q^{4} + 64 q^{9} + 36 q^{15} - 40 q^{16} - 8 q^{22} + 32 q^{23} + 16 q^{25} + 20 q^{29} - 24 q^{36} + 40 q^{39} + 20 q^{44} + 40 q^{51} - 16 q^{53} - 80 q^{57} + 56 q^{58} + 24 q^{60} + 40 q^{64} - 136 q^{71} - 40 q^{72} - 40 q^{74} - 32 q^{78} - 60 q^{79} - 104 q^{81} + 60 q^{85} - 52 q^{86} - 12 q^{88} + 28 q^{92} + 20 q^{93} - 180 q^{95} + 112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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