↑

Properties

Label 3549.2.p
Level $3549$
Weight $2$
Character orbit 3549.p
Rep. character $\chi_{3549}(1084,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $408$
Sturm bound $970$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Sturm bound: \(970\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3549, [\chi])\).

Total New Old
Modular forms 1024 408 616
Cusp forms 912 408 504
Eisenstein series 112 0 112

Trace form

\( 408 q - 4 q^{7} - 408 q^{9} + O(q^{10}) \) \( 408 q - 4 q^{7} - 408 q^{9} - 16 q^{11} + 16 q^{14} - 384 q^{16} - 12 q^{21} - 32 q^{22} - 4 q^{28} - 16 q^{29} - 40 q^{32} + 16 q^{35} + 24 q^{42} - 16 q^{44} + 8 q^{46} - 40 q^{50} + 112 q^{53} - 40 q^{57} - 48 q^{58} + 16 q^{60} + 4 q^{63} + 56 q^{67} + 16 q^{70} - 24 q^{71} + 32 q^{74} - 48 q^{79} + 408 q^{81} - 36 q^{84} + 40 q^{85} - 48 q^{86} - 208 q^{92} - 40 q^{93} - 120 q^{98} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3549, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3549, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)