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Properties

Label 1078.4.bf
Level $1078$
Weight $4$
Character orbit 1078.bf
Rep. character $\chi_{1078}(17,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $8064$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1078.bf (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1078, [\chi])\).

Total New Old
Modular forms 24384 8064 16320
Cusp forms 24000 8064 15936
Eisenstein series 384 0 384

Trace form

\( 8064 q + 672 q^{4} + 48 q^{5} + 20 q^{7} + 1512 q^{9} + O(q^{10}) \) \( 8064 q + 672 q^{4} + 48 q^{5} + 20 q^{7} + 1512 q^{9} + 210 q^{11} + 52 q^{14} + 630 q^{15} - 2688 q^{16} + 2210 q^{17} - 448 q^{20} + 476 q^{22} - 1372 q^{23} + 4508 q^{25} + 968 q^{26} + 252 q^{27} + 120 q^{28} - 700 q^{29} + 1242 q^{31} - 3486 q^{33} + 1880 q^{35} + 12096 q^{36} + 252 q^{37} - 2728 q^{38} - 2640 q^{40} + 3276 q^{42} - 280 q^{44} - 9216 q^{45} + 3740 q^{47} + 8796 q^{49} + 21840 q^{51} - 5040 q^{53} + 924 q^{55} + 224 q^{56} + 560 q^{57} - 10248 q^{58} - 6836 q^{59} - 4368 q^{60} - 4920 q^{61} - 18760 q^{62} - 3100 q^{63} - 21504 q^{64} - 4464 q^{66} - 2240 q^{67} + 120 q^{68} + 3640 q^{69} - 6096 q^{70} - 3360 q^{71} + 1120 q^{72} - 7680 q^{73} + 1400 q^{74} + 4080 q^{75} + 4456 q^{77} + 448 q^{78} + 2100 q^{79} + 1152 q^{80} - 38220 q^{81} + 2088 q^{82} + 800 q^{84} - 8400 q^{85} - 2016 q^{86} - 3920 q^{88} - 9160 q^{89} - 16326 q^{91} + 1792 q^{92} - 2240 q^{93} + 8700 q^{94} - 2660 q^{95} - 72184 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1078, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1078, [\chi])\) into lower level spaces

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