↑

Properties

Label 1078.4.i
Level $1078$
Weight $4$
Character orbit 1078.i
Rep. character $\chi_{1078}(901,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1078.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1040 240 800
Cusp forms 976 240 736
Eisenstein series 64 0 64

Trace form

\( 240 q + 480 q^{4} - 48 q^{5} + 1208 q^{9} + O(q^{10}) \) \( 240 q + 480 q^{4} - 48 q^{5} + 1208 q^{9} + 2 q^{11} + 152 q^{15} - 1920 q^{16} - 176 q^{22} + 196 q^{23} + 2548 q^{25} + 696 q^{26} + 828 q^{31} - 1314 q^{33} + 9664 q^{36} + 180 q^{37} - 744 q^{38} - 8 q^{44} - 3552 q^{45} - 912 q^{47} + 1372 q^{53} - 840 q^{58} + 3000 q^{59} + 304 q^{60} - 15360 q^{64} + 384 q^{66} + 1296 q^{67} + 5840 q^{71} + 13680 q^{75} + 1920 q^{78} + 768 q^{80} - 5616 q^{81} + 672 q^{82} + 632 q^{86} - 352 q^{88} - 8520 q^{89} + 1568 q^{92} - 9080 q^{93} - 5960 q^{99} + O(q^{100}) \)

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

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