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Properties

Label 1300.2.v
Level $1300$
Weight $2$
Character orbit 1300.v
Rep. character $\chi_{1300}(261,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $120$
Sturm bound $420$

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Defining parameters

Level: \( N \) \(=\) \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1300.v (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(420\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1300, [\chi])\).

Total New Old
Modular forms 864 120 744
Cusp forms 816 120 696
Eisenstein series 48 0 48

Trace form

\( 120 q - 4 q^{3} + 6 q^{5} + 4 q^{7} - 34 q^{9} + O(q^{10}) \) \( 120 q - 4 q^{3} + 6 q^{5} + 4 q^{7} - 34 q^{9} + 10 q^{11} - 6 q^{17} + 4 q^{19} - 4 q^{21} - 10 q^{23} + 32 q^{25} + 56 q^{27} + 6 q^{29} - 24 q^{31} + 4 q^{33} + 18 q^{35} + 4 q^{37} + 16 q^{41} - 88 q^{43} - 84 q^{45} - 20 q^{47} + 108 q^{49} + 12 q^{51} + 14 q^{53} - 32 q^{55} - 140 q^{57} - 6 q^{59} + 20 q^{61} + 86 q^{63} - 2 q^{65} + 42 q^{67} + 38 q^{69} - 26 q^{71} + 12 q^{73} + 36 q^{75} + 60 q^{77} + 52 q^{79} - 48 q^{81} + 22 q^{83} + 78 q^{85} - 80 q^{87} - 8 q^{89} + 4 q^{91} - 40 q^{93} - 6 q^{95} - 22 q^{97} - 120 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1300, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)