Properties

Label 1380.2.y
Level $1380$
Weight $2$
Character orbit 1380.y
Rep. character $\chi_{1380}(121,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $160$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.y (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1380, [\chi])\).

Total New Old
Modular forms 3000 160 2840
Cusp forms 2760 160 2600
Eisenstein series 240 0 240

Trace form

\( 160q - 16q^{9} + O(q^{10}) \) \( 160q - 16q^{9} + 8q^{13} - 28q^{17} - 44q^{19} - 16q^{25} - 32q^{29} - 56q^{31} - 8q^{33} + 40q^{35} - 16q^{37} + 36q^{39} + 76q^{41} + 64q^{43} - 24q^{47} - 28q^{49} + 80q^{51} + 80q^{53} + 44q^{55} - 8q^{57} + 40q^{59} - 44q^{61} - 52q^{67} + 4q^{71} - 36q^{73} + 24q^{77} + 44q^{79} - 16q^{81} + 104q^{83} + 4q^{85} + 8q^{87} + 96q^{89} + 16q^{91} - 16q^{93} + 16q^{95} + 56q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)