↑

Properties

Label 1300.2.cz
Level $1300$
Weight $2$
Character orbit 1300.cz
Rep. character $\chi_{1300}(33,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $560$
Sturm bound $420$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1300.cz (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(420\)

Dimensions

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

Total New Old
Modular forms 3456 560 2896
Cusp forms 3264 560 2704
Eisenstein series 192 0 192

Trace form

\( 560 q + O(q^{10}) \) \( 560 q - 12 q^{13} - 28 q^{15} + 2 q^{17} - 20 q^{19} + 12 q^{23} - 2 q^{25} + 24 q^{27} + 20 q^{29} - 66 q^{33} + 12 q^{35} - 42 q^{37} - 40 q^{39} - 70 q^{41} - 48 q^{45} + 50 q^{47} + 280 q^{49} - 6 q^{53} + 86 q^{55} + 56 q^{57} - 118 q^{63} - 30 q^{65} - 32 q^{67} + 210 q^{69} - 60 q^{73} - 26 q^{75} - 8 q^{77} + 50 q^{81} + 70 q^{83} - 46 q^{85} - 4 q^{87} - 70 q^{89} + 120 q^{91} + 36 q^{93} + 32 q^{95} - 56 q^{97} + O(q^{100}) \)

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

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