Properties

Label 2300.2.bo
Level $2300$
Weight $2$
Character orbit 2300.bo
Rep. character $\chi_{2300}(9,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $2400$
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.bo (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 575 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 14640 2400 12240
Cusp forms 14160 2400 11760
Eisenstein series 480 0 480

Trace form

\( 2400q - 10q^{5} - 64q^{9} + O(q^{10}) \) \( 2400q - 10q^{5} - 64q^{9} - 10q^{11} + 31q^{15} + 10q^{17} + 16q^{19} - 8q^{21} - 90q^{23} - 4q^{25} + 30q^{27} + 12q^{29} + 12q^{31} + 20q^{33} - 24q^{39} + 2q^{45} + 200q^{47} + 220q^{49} + 32q^{51} - 20q^{53} - 26q^{55} - 18q^{59} - 8q^{61} - 90q^{63} - 39q^{65} - 30q^{67} + 171q^{69} + 102q^{71} + 80q^{73} + 272q^{75} + 40q^{77} + 16q^{79} - 70q^{81} + 50q^{83} - 88q^{85} + 60q^{87} + 44q^{89} + 12q^{91} + 139q^{95} - 30q^{97} + 102q^{99} + O(q^{100}) \)

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

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