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Properties

Label 1610.2.u
Level $1610$
Weight $2$
Character orbit 1610.u
Rep. character $\chi_{1610}(71,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $480$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1610 = 2 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1610.u (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1610, [\chi])\).

Total New Old
Modular forms 2960 480 2480
Cusp forms 2800 480 2320
Eisenstein series 160 0 160

Trace form

\( 480 q - 48 q^{4} - 48 q^{9} + O(q^{10}) \) \( 480 q - 48 q^{4} - 48 q^{9} - 16 q^{11} - 16 q^{13} - 48 q^{16} + 56 q^{17} + 72 q^{19} + 80 q^{22} - 24 q^{23} - 48 q^{25} + 72 q^{26} - 48 q^{27} + 24 q^{29} - 8 q^{30} + 40 q^{31} - 48 q^{33} - 16 q^{34} - 48 q^{36} - 24 q^{37} - 32 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{42} + 64 q^{43} - 16 q^{44} - 32 q^{45} - 24 q^{46} - 96 q^{47} - 48 q^{49} + 8 q^{51} - 16 q^{52} - 48 q^{54} + 72 q^{55} + 120 q^{57} - 64 q^{58} + 96 q^{59} - 48 q^{61} + 200 q^{62} - 32 q^{63} - 48 q^{64} - 32 q^{65} + 96 q^{66} + 104 q^{67} - 32 q^{68} - 96 q^{69} - 80 q^{71} + 80 q^{73} + 144 q^{74} - 16 q^{76} + 200 q^{78} + 8 q^{79} + 32 q^{81} - 32 q^{82} + 272 q^{83} - 32 q^{86} - 32 q^{87} - 8 q^{88} - 8 q^{89} - 32 q^{90} - 16 q^{91} - 24 q^{92} - 64 q^{93} - 16 q^{94} - 32 q^{95} - 40 q^{97} - 128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1610, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1610, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1610, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(805, [\chi])\)\(^{\oplus 2}\)