Properties

Label 1078.2.o
Level $1078$
Weight $2$
Character orbit 1078.o
Rep. character $\chi_{1078}(153,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $336$
Sturm bound $336$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.o (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 1032 336 696
Cusp forms 984 336 648
Eisenstein series 48 0 48

Trace form

\( 336 q + 56 q^{4} + 56 q^{9} + O(q^{10}) \) \( 336 q + 56 q^{4} + 56 q^{9} + 6 q^{11} - 8 q^{14} - 20 q^{15} - 56 q^{16} + 28 q^{20} + 14 q^{22} + 52 q^{23} + 56 q^{25} + 28 q^{26} + 84 q^{27} - 56 q^{36} + 16 q^{37} + 28 q^{38} - 116 q^{42} - 6 q^{44} + 112 q^{45} - 56 q^{47} + 72 q^{49} - 112 q^{53} - 168 q^{55} - 20 q^{56} - 60 q^{58} - 28 q^{59} + 20 q^{60} + 56 q^{64} + 8 q^{67} - 56 q^{69} + 4 q^{70} - 8 q^{71} - 46 q^{77} - 32 q^{78} - 160 q^{81} + 60 q^{86} + 14 q^{88} - 168 q^{89} + 164 q^{91} + 32 q^{92} + 24 q^{93} - 144 q^{99} + O(q^{100}) \)

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

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