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Properties

Label 1035.3.bd
Level $1035$
Weight $3$
Character orbit 1035.bd
Rep. character $\chi_{1035}(19,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1180$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1035.bd (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1035, [\chi])\).

Total New Old
Modular forms 2960 1220 1740
Cusp forms 2800 1180 1620
Eisenstein series 160 40 120

Trace form

\( 1180 q + 210 q^{4} + 11 q^{5} + O(q^{10}) \) \( 1180 q + 210 q^{4} + 11 q^{5} - 11 q^{10} + 22 q^{11} + 22 q^{14} - 438 q^{16} - 22 q^{19} - 77 q^{20} + 25 q^{25} + 102 q^{26} - 16 q^{29} + 8 q^{31} + 220 q^{34} - 95 q^{35} - 11 q^{40} + 100 q^{41} - 22 q^{44} - 222 q^{46} - 518 q^{49} - 141 q^{50} + 87 q^{55} - 770 q^{56} + 392 q^{59} - 330 q^{61} + 734 q^{64} + 242 q^{65} - 738 q^{70} + 366 q^{71} - 506 q^{74} - 968 q^{76} - 506 q^{79} - 220 q^{80} + 121 q^{85} - 682 q^{86} + 22 q^{89} + 366 q^{94} + 164 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1035, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1035, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1035, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)