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Properties

Label 1078.4.ba
Level $1078$
Weight $4$
Character orbit 1078.ba
Rep. character $\chi_{1078}(13,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $4032$
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.ba (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{70})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 12192 4032 8160
Cusp forms 12000 4032 7968
Eisenstein series 192 0 192

Trace form

\( 4032 q - 672 q^{4} - 20 q^{7} - 1512 q^{9} + O(q^{10}) \) \( 4032 q - 672 q^{4} - 20 q^{7} - 1512 q^{9} - 168 q^{11} - 52 q^{14} - 630 q^{15} + 2688 q^{16} - 2240 q^{17} + 448 q^{20} - 476 q^{22} + 784 q^{23} - 3584 q^{25} - 1064 q^{26} - 252 q^{27} - 120 q^{28} + 700 q^{29} - 1010 q^{35} + 6048 q^{36} + 504 q^{37} - 1736 q^{38} - 1680 q^{40} - 3708 q^{42} + 616 q^{44} - 2352 q^{45} + 1036 q^{47} + 4974 q^{49} + 8400 q^{51} + 4032 q^{53} - 2184 q^{55} + 352 q^{56} - 560 q^{57} + 4200 q^{58} + 3836 q^{59} - 1680 q^{60} - 9380 q^{62} - 6440 q^{63} - 10752 q^{64} - 4480 q^{67} - 3640 q^{69} + 7644 q^{70} + 3360 q^{71} + 2240 q^{72} + 13440 q^{73} + 2800 q^{74} + 5078 q^{77} - 448 q^{78} + 4200 q^{79} + 8484 q^{81} + 400 q^{84} + 8400 q^{85} + 1260 q^{86} + 1568 q^{88} + 17080 q^{89} + 9666 q^{91} - 1792 q^{92} - 4480 q^{93} - 27300 q^{94} - 5320 q^{95} + 72184 q^{99} + O(q^{100}) \)

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

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