Properties

Label 1859.2.w
Level $1859$
Weight $2$
Character orbit 1859.w
Rep. character $\chi_{1859}(12,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $1824$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.w (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{26})\)
Sturm bound: \(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1859, [\chi])\).

Total New Old
Modular forms 2208 1824 384
Cusp forms 2160 1824 336
Eisenstein series 48 0 48

Trace form

\( 1824 q + 4 q^{3} + 154 q^{4} - 152 q^{9} + O(q^{10}) \) \( 1824 q + 4 q^{3} + 154 q^{4} - 152 q^{9} - 8 q^{10} - 122 q^{13} - 104 q^{15} - 150 q^{16} + 12 q^{17} - 78 q^{18} - 24 q^{22} + 156 q^{23} + 156 q^{24} + 152 q^{25} - 10 q^{26} + 40 q^{27} - 4 q^{29} + 88 q^{30} - 26 q^{32} + 146 q^{36} + 102 q^{38} + 100 q^{39} - 172 q^{40} - 236 q^{42} - 16 q^{43} + 130 q^{45} + 130 q^{47} - 10 q^{48} + 108 q^{49} - 142 q^{51} - 36 q^{52} - 54 q^{53} - 156 q^{54} + 8 q^{55} - 32 q^{56} - 104 q^{58} - 104 q^{59} + 12 q^{61} + 48 q^{62} + 138 q^{64} + 20 q^{65} + 8 q^{66} - 186 q^{68} - 52 q^{69} + 44 q^{74} - 186 q^{75} - 8 q^{77} - 6 q^{78} + 60 q^{79} - 104 q^{81} + 24 q^{82} - 494 q^{84} - 78 q^{85} - 4 q^{87} - 30 q^{88} - 80 q^{90} - 104 q^{91} + 44 q^{92} - 156 q^{93} + 72 q^{94} - 16 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1859, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1859, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1859, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)