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Properties

Label 1155.2.z
Level $1155$
Weight $2$
Character orbit 1155.z
Rep. character $\chi_{1155}(421,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $192$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.z (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1155, [\chi])\).

Total New Old
Modular forms 800 192 608
Cusp forms 736 192 544
Eisenstein series 64 0 64

Trace form

\( 192 q - 8 q^{2} - 56 q^{4} - 8 q^{7} + 16 q^{8} - 48 q^{9} + O(q^{10}) \) \( 192 q - 8 q^{2} - 56 q^{4} - 8 q^{7} + 16 q^{8} - 48 q^{9} + 24 q^{11} + 24 q^{13} + 12 q^{14} - 32 q^{16} - 16 q^{17} + 12 q^{18} - 8 q^{22} + 32 q^{23} - 48 q^{25} - 16 q^{26} - 4 q^{28} - 32 q^{29} - 8 q^{30} - 24 q^{31} - 96 q^{32} - 8 q^{33} - 96 q^{34} - 56 q^{36} + 72 q^{37} + 104 q^{38} - 16 q^{39} - 16 q^{41} + 96 q^{43} - 76 q^{44} - 36 q^{46} + 80 q^{47} - 64 q^{48} - 48 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 24 q^{56} - 16 q^{57} + 52 q^{58} - 64 q^{59} + 32 q^{61} - 80 q^{62} - 8 q^{63} - 24 q^{64} - 16 q^{66} - 32 q^{67} - 64 q^{68} + 8 q^{71} - 4 q^{72} + 32 q^{73} + 104 q^{74} + 176 q^{76} - 16 q^{77} - 80 q^{78} - 16 q^{79} - 48 q^{81} + 88 q^{82} - 16 q^{83} - 16 q^{85} - 44 q^{86} - 16 q^{87} - 96 q^{88} + 160 q^{89} - 60 q^{92} - 32 q^{93} - 48 q^{94} + 120 q^{96} - 24 q^{97} - 8 q^{98} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1155, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1155, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1155, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)