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Properties

Label 1155.2.v
Level $1155$
Weight $2$
Character orbit 1155.v
Rep. character $\chi_{1155}(727,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $160$
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.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 400 160 240
Cusp forms 368 160 208
Eisenstein series 32 0 32

Trace form

\( 160 q - 48 q^{8} + O(q^{10}) \) \( 160 q - 48 q^{8} - 128 q^{16} - 16 q^{21} + 16 q^{23} + 8 q^{28} - 96 q^{32} + 48 q^{35} - 160 q^{36} + 40 q^{42} + 48 q^{43} + 144 q^{50} - 48 q^{53} - 48 q^{56} - 104 q^{58} - 80 q^{60} + 64 q^{67} + 24 q^{70} - 64 q^{71} - 48 q^{72} + 40 q^{78} - 160 q^{81} + 48 q^{85} + 24 q^{88} + 80 q^{91} - 80 q^{92} + 160 q^{95} + 56 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1155, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)