Properties

Label 1155.2.bl
Level $1155$
Weight $2$
Character orbit 1155.bl
Rep. character $\chi_{1155}(241,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Sturm bound $384$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 400 128 272
Cusp forms 368 128 240
Eisenstein series 32 0 32

Trace form

\( 128 q + 72 q^{4} + 64 q^{9} + O(q^{10}) \) \( 128 q + 72 q^{4} + 64 q^{9} + 4 q^{11} + 40 q^{14} - 64 q^{16} - 40 q^{22} - 16 q^{23} + 64 q^{25} + 24 q^{26} + 144 q^{36} + 24 q^{37} - 48 q^{38} + 40 q^{42} + 4 q^{44} - 24 q^{47} + 8 q^{49} - 72 q^{53} + 32 q^{56} - 8 q^{58} + 48 q^{59} - 144 q^{64} + 36 q^{66} - 24 q^{67} - 8 q^{70} - 48 q^{71} + 12 q^{77} + 48 q^{78} + 48 q^{80} - 64 q^{81} + 48 q^{82} - 120 q^{86} - 128 q^{88} - 120 q^{89} + 88 q^{91} + 192 q^{92} + 16 q^{93} + 8 q^{99} + O(q^{100}) \)

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

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