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Properties

Label 1500.2.m
Level $1500$
Weight $2$
Character orbit 1500.m
Rep. character $\chi_{1500}(301,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $64$
Newform subspaces $4$
Sturm bound $600$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1500.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
Sturm bound: \(600\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1500, [\chi])\).

Total New Old
Modular forms 1320 64 1256
Cusp forms 1080 64 1016
Eisenstein series 240 0 240

Trace form

\( 64 q - 16 q^{9} + O(q^{10}) \) \( 64 q - 16 q^{9} - 6 q^{11} - 10 q^{17} - 10 q^{19} - 4 q^{21} + 16 q^{29} + 6 q^{31} - 10 q^{33} + 10 q^{37} + 10 q^{41} + 80 q^{43} + 40 q^{47} + 96 q^{49} + 16 q^{51} + 30 q^{53} + 36 q^{59} + 8 q^{61} - 10 q^{63} - 20 q^{67} - 4 q^{69} + 40 q^{71} + 20 q^{73} - 40 q^{77} - 8 q^{79} - 16 q^{81} - 10 q^{83} + 20 q^{87} - 30 q^{89} - 30 q^{91} + 40 q^{93} - 20 q^{97} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1500, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1500.2.m.a 1500.m 25.d $8$ $11.978$ 8.0.26265625.1 None \(0\) \(-2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{6}q^{3}+(-1-\beta _{2}-\beta _{6}+\beta _{7})q^{7}+\cdots\)
1500.2.m.b 1500.m 25.d $8$ $11.978$ \(\Q(\zeta_{15})\) None \(0\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\zeta_{15}^{2}+\zeta_{15}^{4}+\zeta_{15}^{5})q^{3}+(\zeta_{15}+\cdots)q^{7}+\cdots\)
1500.2.m.c 1500.m 25.d $24$ $11.978$ None \(0\) \(-6\) \(0\) \(16\) $\mathrm{SU}(2)[C_{5}]$
1500.2.m.d 1500.m 25.d $24$ $11.978$ None \(0\) \(6\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1500, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1500, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(750, [\chi])\)\(^{\oplus 2}\)