Properties

Label 2601.2.f
Level $2601$
Weight $2$
Character orbit 2601.f
Rep. character $\chi_{2601}(829,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $212$
Sturm bound $612$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Sturm bound: \(612\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2601, [\chi])\).

Total New Old
Modular forms 684 240 444
Cusp forms 540 212 328
Eisenstein series 144 28 116

Trace form

\( 212q - 196q^{4} - 4q^{5} + O(q^{10}) \) \( 212q - 196q^{4} - 4q^{5} + 4q^{10} + 12q^{13} + 24q^{14} + 180q^{16} - 12q^{20} - 8q^{22} - 16q^{23} + 8q^{28} + 4q^{29} - 8q^{31} + 48q^{35} - 12q^{37} - 48q^{38} - 28q^{40} + 28q^{41} - 32q^{44} - 12q^{47} - 72q^{50} - 32q^{52} + 28q^{55} - 24q^{56} - 28q^{58} + 4q^{61} + 16q^{62} - 60q^{64} + 16q^{65} + 20q^{67} + 24q^{71} + 12q^{73} - 28q^{74} + 60q^{80} - 4q^{82} + 12q^{86} + 16q^{88} - 20q^{89} + 40q^{91} + 56q^{92} + 8q^{95} - 28q^{97} - 104q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2601, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2601, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2601, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(867, [\chi])\)\(^{\oplus 2}\)