Properties

Label 1200.2.bo
Level $1200$
Weight $2$
Character orbit 1200.bo
Rep. character $\chi_{1200}(241,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $120$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1200.bo (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1200, [\chi])\).

Total New Old
Modular forms 1008 120 888
Cusp forms 912 120 792
Eisenstein series 96 0 96

Trace form

\( 120 q + 2 q^{5} - 30 q^{9} + O(q^{10}) \) \( 120 q + 2 q^{5} - 30 q^{9} + 4 q^{13} - 4 q^{17} - 12 q^{19} + 36 q^{23} + 2 q^{25} + 4 q^{29} + 12 q^{31} + 8 q^{33} - 6 q^{37} + 8 q^{39} - 4 q^{41} + 16 q^{43} + 2 q^{45} + 24 q^{47} + 128 q^{49} + 48 q^{51} - 6 q^{53} - 16 q^{55} + 4 q^{61} + 38 q^{65} - 60 q^{67} - 12 q^{73} + 8 q^{75} + 20 q^{79} - 30 q^{81} + 76 q^{83} + 2 q^{85} + 36 q^{87} + 30 q^{89} - 24 q^{91} - 64 q^{93} + 28 q^{95} + 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)