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Properties

Label 1205.2.co
Level $1205$
Weight $2$
Character orbit 1205.co
Rep. character $\chi_{1205}(161,\cdot)$
Character field $\Q(\zeta_{120})$
Dimension $2560$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.co (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{120})\)
Sturm bound: \(242\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1205, [\chi])\).

Total New Old
Modular forms 3968 2560 1408
Cusp forms 3840 2560 1280
Eisenstein series 128 0 128

Trace form

\( 2560 q - 24 q^{4} - 24 q^{9} + O(q^{10}) \) \( 2560 q - 24 q^{4} - 24 q^{9} + 8 q^{10} - 40 q^{12} + 104 q^{14} + 64 q^{15} + 1176 q^{16} - 8 q^{17} + 8 q^{19} + 8 q^{21} + 48 q^{22} + 56 q^{23} + 8 q^{26} + 48 q^{27} - 48 q^{28} - 40 q^{29} - 8 q^{30} - 272 q^{31} - 120 q^{33} - 80 q^{34} + 336 q^{36} - 16 q^{39} - 16 q^{41} - 48 q^{42} + 16 q^{43} - 48 q^{44} - 152 q^{46} + 32 q^{47} + 320 q^{48} - 112 q^{49} + 112 q^{51} + 80 q^{52} - 112 q^{56} + 32 q^{57} + 16 q^{58} - 16 q^{59} - 24 q^{60} + 8 q^{61} - 56 q^{62} - 40 q^{63} - 32 q^{65} - 40 q^{67} - 128 q^{68} - 272 q^{69} - 24 q^{70} + 8 q^{71} - 24 q^{73} + 32 q^{74} - 120 q^{76} - 128 q^{78} + 8 q^{79} - 256 q^{80} - 672 q^{81} - 24 q^{82} - 8 q^{84} + 112 q^{86} + 112 q^{87} - 72 q^{88} - 64 q^{89} - 80 q^{91} - 352 q^{92} + 8 q^{93} - 16 q^{94} + 160 q^{98} - 224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1205, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1205, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(241, [\chi])\)\(^{\oplus 2}\)