Properties

Label 2300.2.bs
Level $2300$
Weight $2$
Character orbit 2300.bs
Rep. character $\chi_{2300}(17,\cdot)$
Character field $\Q(\zeta_{220})$
Dimension $4800$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2300.bs (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 575 \)
Character field: \(\Q(\zeta_{220})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2300, [\chi])\).

Total New Old
Modular forms 29280 4800 24480
Cusp forms 28320 4800 23520
Eisenstein series 960 0 960

Trace form

\( 4800 q - 4 q^{3} + O(q^{10}) \) \( 4800 q - 4 q^{3} + 8 q^{13} + 154 q^{23} - 36 q^{25} - 40 q^{27} + 40 q^{29} - 22 q^{33} + 16 q^{35} + 88 q^{37} + 80 q^{39} - 308 q^{47} - 4 q^{55} + 88 q^{57} + 60 q^{59} + 70 q^{69} - 180 q^{71} + 60 q^{73} + 68 q^{75} + 44 q^{77} - 160 q^{81} + 28 q^{85} - 96 q^{87} + 148 q^{93} - 274 q^{95} + 66 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2300, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 2}\)