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Properties

Label 1521.2.bt
Level $1521$
Weight $2$
Character orbit 1521.bt
Rep. character $\chi_{1521}(10,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $1800$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1521.bt (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 4464 1848 2616
Cusp forms 4272 1800 2472
Eisenstein series 192 48 144

Trace form

\( 1800 q + 23 q^{2} - 99 q^{4} + 26 q^{5} - 20 q^{7} + 26 q^{8} + O(q^{10}) \) \( 1800 q + 23 q^{2} - 99 q^{4} + 26 q^{5} - 20 q^{7} + 26 q^{8} - 29 q^{10} + 20 q^{11} + 32 q^{13} + 22 q^{14} + 41 q^{16} + 27 q^{17} - 21 q^{19} + 41 q^{20} - 21 q^{22} - 55 q^{23} + 118 q^{25} + 29 q^{26} + 22 q^{28} + 21 q^{29} + 26 q^{31} + 160 q^{32} - 91 q^{34} + 16 q^{35} - 35 q^{37} + 113 q^{38} - 28 q^{40} + 5 q^{41} - 22 q^{43} - 42 q^{46} - 117 q^{47} - 191 q^{49} + 20 q^{50} + 45 q^{52} - 11 q^{53} - 108 q^{55} + 30 q^{56} + 47 q^{58} + 240 q^{59} - 23 q^{61} + 95 q^{62} + 28 q^{64} + 23 q^{65} - 66 q^{67} - 30 q^{68} + 92 q^{71} - 26 q^{73} + 35 q^{74} - 322 q^{76} + 38 q^{77} - 58 q^{79} - 173 q^{82} - 234 q^{83} - 26 q^{85} + 104 q^{86} + 260 q^{88} + 39 q^{89} - 12 q^{91} - 46 q^{92} - 20 q^{94} + 211 q^{95} + 58 q^{97} + 47 q^{98} + O(q^{100}) \)

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

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