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Properties

Label 2300.2.m
Level $2300$
Weight $2$
Character orbit 2300.m
Rep. character $\chi_{2300}(461,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $216$
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.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1464 216 1248
Cusp forms 1416 216 1200
Eisenstein series 48 0 48

Trace form

\( 216 q + 2 q^{5} + 8 q^{7} - 50 q^{9} + O(q^{10}) \) \( 216 q + 2 q^{5} + 8 q^{7} - 50 q^{9} + 12 q^{13} - 2 q^{15} - 8 q^{17} - 12 q^{21} + 10 q^{25} + 42 q^{27} + 24 q^{29} - 12 q^{31} + 62 q^{33} - 10 q^{35} - 30 q^{37} - 20 q^{39} + 46 q^{41} - 128 q^{45} + 6 q^{47} + 192 q^{49} + 4 q^{51} - 62 q^{53} + 14 q^{55} - 176 q^{57} + 44 q^{61} + 86 q^{63} + 34 q^{65} + 8 q^{67} + 8 q^{69} - 10 q^{71} - 16 q^{73} + 28 q^{75} + 68 q^{77} + 32 q^{79} - 54 q^{81} + 6 q^{83} - 12 q^{85} + 10 q^{87} - 12 q^{91} - 8 q^{93} - 12 q^{95} + 8 q^{97} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(2300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)