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Properties

Label 1155.2.dr
Level $1155$
Weight $2$
Character orbit 1155.dr
Rep. character $\chi_{1155}(172,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1536$
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.dr (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 3200 1536 1664
Cusp forms 2944 1536 1408
Eisenstein series 256 0 256

Trace form

\( 1536 q - 8 q^{5} + 20 q^{7} + O(q^{10}) \) \( 1536 q - 8 q^{5} + 20 q^{7} + 8 q^{11} + 24 q^{15} - 208 q^{16} + 40 q^{17} - 24 q^{22} + 32 q^{23} + 16 q^{25} + 48 q^{26} + 60 q^{28} - 12 q^{33} + 384 q^{36} + 40 q^{37} + 240 q^{41} - 12 q^{42} + 240 q^{46} - 80 q^{47} + 40 q^{51} - 8 q^{55} - 352 q^{56} + 36 q^{58} - 80 q^{61} - 20 q^{63} + 24 q^{66} - 32 q^{67} - 160 q^{68} - 140 q^{70} - 64 q^{71} + 120 q^{73} - 16 q^{75} + 116 q^{77} - 192 q^{78} - 120 q^{80} - 192 q^{81} - 16 q^{82} - 160 q^{85} + 80 q^{86} - 8 q^{88} - 8 q^{91} + 160 q^{92} + 72 q^{93} - 20 q^{95} - 32 q^{97} + O(q^{100}) \)

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

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