Properties

Label 2300.2.bk
Level $2300$
Weight $2$
Character orbit 2300.bk
Rep. character $\chi_{2300}(41,\cdot)$
Character field $\Q(\zeta_{55})$
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.bk (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 575 \)
Character field: \(\Q(\zeta_{55})\)
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

\( 2400 q - 4 q^{3} + 6 q^{5} - 4 q^{7} + 56 q^{9} + O(q^{10}) \) \( 2400 q - 4 q^{3} + 6 q^{5} - 4 q^{7} + 56 q^{9} + 10 q^{11} - 8 q^{13} - 23 q^{15} + 6 q^{17} + 16 q^{19} + 8 q^{21} - 60 q^{23} + 64 q^{25} + 26 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{33} + 16 q^{35} - 84 q^{37} - 24 q^{39} - 100 q^{43} - 14 q^{45} + 124 q^{47} - 260 q^{49} - 32 q^{51} + 20 q^{53} - 2 q^{55} - 56 q^{57} - 18 q^{59} + 8 q^{61} - 22 q^{63} + 79 q^{65} + 66 q^{67} - 129 q^{69} + 78 q^{71} - 20 q^{73} - 212 q^{75} + 52 q^{77} + 16 q^{79} + 150 q^{81} + 86 q^{83} + 44 q^{85} - 124 q^{87} + 4 q^{89} - 12 q^{91} - 36 q^{93} + 187 q^{95} + 72 q^{97} + 62 q^{99} + O(q^{100}) \)

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

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