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Properties

Label 1155.2.cy
Level $1155$
Weight $2$
Character orbit 1155.cy
Rep. character $\chi_{1155}(61,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $512$
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.cy (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 1600 512 1088
Cusp forms 1472 512 960
Eisenstein series 128 0 128

Trace form

\( 512 q - 72 q^{4} + 80 q^{8} - 64 q^{9} + O(q^{10}) \) \( 512 q - 72 q^{4} + 80 q^{8} - 64 q^{9} - 4 q^{11} - 20 q^{14} + 24 q^{16} + 120 q^{17} + 20 q^{18} - 80 q^{22} + 16 q^{23} + 180 q^{24} - 64 q^{25} - 24 q^{26} - 80 q^{29} - 144 q^{36} + 56 q^{37} + 48 q^{38} - 40 q^{42} + 16 q^{44} - 20 q^{46} + 24 q^{47} + 112 q^{49} + 20 q^{51} - 8 q^{53} + 128 q^{56} + 28 q^{58} - 48 q^{59} + 104 q^{64} - 36 q^{66} - 16 q^{67} - 360 q^{68} - 52 q^{70} + 128 q^{71} - 20 q^{72} - 180 q^{73} - 80 q^{74} - 12 q^{77} - 48 q^{78} - 100 q^{79} - 48 q^{80} + 64 q^{81} - 288 q^{82} + 120 q^{84} - 180 q^{86} + 48 q^{88} + 12 q^{91} + 248 q^{92} - 16 q^{93} - 60 q^{94} + 72 q^{99} + O(q^{100}) \)

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

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