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Properties

Label 1521.2.q
Level $1521$
Weight $2$
Character orbit 1521.q
Rep. character $\chi_{1521}(316,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $118$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1521.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1521, [\chi])\).

Total New Old
Modular forms 420 138 282
Cusp forms 308 118 190
Eisenstein series 112 20 92

Trace form

\( 118 q - 3 q^{2} + 55 q^{4} + 6 q^{7} + O(q^{10}) \) \( 118 q - 3 q^{2} + 55 q^{4} + 6 q^{7} - 11 q^{10} - 6 q^{11} + 28 q^{14} - 41 q^{16} + 5 q^{17} + 18 q^{19} + 15 q^{20} + 22 q^{22} + 14 q^{23} - 84 q^{25} + 48 q^{28} - 13 q^{29} - 9 q^{32} - 2 q^{35} - 9 q^{37} + 28 q^{38} - 74 q^{40} - 21 q^{41} - 8 q^{43} - 42 q^{46} + 7 q^{49} - 6 q^{50} + 58 q^{53} + 20 q^{55} + 20 q^{56} + 21 q^{58} + 6 q^{59} - q^{61} + 8 q^{62} - 122 q^{64} + 12 q^{67} - 63 q^{68} - 12 q^{71} - 13 q^{74} + 42 q^{76} + 12 q^{77} - 80 q^{79} - 39 q^{80} - 45 q^{82} - 39 q^{85} - 14 q^{88} + 20 q^{92} + 20 q^{94} + 20 q^{95} + 6 q^{97} + 21 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1521, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)