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Properties

Label 1078.2.ba
Level $1078$
Weight $2$
Character orbit 1078.ba
Rep. character $\chi_{1078}(13,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $1344$
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.ba (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{70})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 4128 1344 2784
Cusp forms 3936 1344 2592
Eisenstein series 192 0 192

Trace form

\( 1344 q - 56 q^{4} - 10 q^{7} - 56 q^{9} + O(q^{10}) \) \( 1344 q - 56 q^{4} - 10 q^{7} - 56 q^{9} - 6 q^{11} - 2 q^{14} - 30 q^{15} + 56 q^{16} - 70 q^{17} - 28 q^{20} - 14 q^{22} - 52 q^{23} - 56 q^{25} - 28 q^{26} + 126 q^{27} + 10 q^{28} + 20 q^{29} + 60 q^{35} + 56 q^{36} - 16 q^{37} - 28 q^{38} - 70 q^{40} + 126 q^{42} + 26 q^{44} - 112 q^{45} - 154 q^{47} - 112 q^{49} - 200 q^{51} + 152 q^{53} + 168 q^{55} + 20 q^{56} - 80 q^{57} - 140 q^{58} + 28 q^{59} - 20 q^{60} - 70 q^{62} - 40 q^{63} - 56 q^{64} + 32 q^{67} + 56 q^{69} + 26 q^{70} - 72 q^{71} - 40 q^{72} - 210 q^{73} - 40 q^{74} + 46 q^{77} + 32 q^{78} - 60 q^{79} - 100 q^{81} - 20 q^{84} + 100 q^{85} + 90 q^{86} + 36 q^{88} + 168 q^{89} - 184 q^{91} + 28 q^{92} - 84 q^{93} + 350 q^{94} - 20 q^{95} - 816 q^{99} + O(q^{100}) \)

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

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