Properties

Label 1078.2.s
Level $1078$
Weight $2$
Character orbit 1078.s
Rep. character $\chi_{1078}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $320$
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.s (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 320 q - 40 q^{4} - 12 q^{5} - 64 q^{9} + O(q^{10}) \) \( 320 q - 40 q^{4} - 12 q^{5} - 64 q^{9} + 12 q^{11} + 36 q^{15} + 40 q^{16} + 30 q^{17} - 16 q^{22} + 16 q^{23} - 16 q^{25} + 24 q^{26} - 20 q^{29} + 18 q^{31} + 126 q^{33} - 48 q^{36} - 24 q^{37} + 12 q^{38} - 40 q^{39} + 30 q^{40} - 2 q^{44} - 108 q^{45} + 24 q^{47} + 80 q^{51} - 8 q^{53} + 80 q^{57} + 28 q^{58} + 60 q^{59} - 12 q^{60} - 30 q^{61} + 80 q^{64} - 72 q^{66} + 48 q^{67} - 30 q^{68} - 56 q^{71} - 20 q^{72} - 90 q^{73} - 20 q^{74} - 180 q^{75} - 160 q^{78} - 30 q^{79} - 18 q^{80} - 4 q^{81} - 60 q^{82} - 180 q^{85} - 2 q^{86} - 18 q^{88} + 36 q^{89} - 28 q^{92} - 146 q^{93} + 120 q^{94} + 150 q^{95} - 16 q^{99} + O(q^{100}) \)

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

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