↑

Properties

Label 350.3.i
Level $350$
Weight $3$
Character orbit 350.i
Rep. character $\chi_{350}(199,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $3$
Sturm bound $180$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 350.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(180\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(350, [\chi])\).

Total New Old
Modular forms 264 48 216
Cusp forms 216 48 168
Eisenstein series 48 0 48

Trace form

\( 48 q + 48 q^{4} - 96 q^{9} + O(q^{10}) \) \( 48 q + 48 q^{4} - 96 q^{9} + 4 q^{11} - 64 q^{14} - 96 q^{16} + 84 q^{19} + 16 q^{21} + 48 q^{24} + 96 q^{26} + 192 q^{29} - 48 q^{31} - 384 q^{36} - 264 q^{39} - 8 q^{44} + 56 q^{46} - 232 q^{49} + 32 q^{51} + 216 q^{54} - 112 q^{56} + 504 q^{59} + 264 q^{61} - 384 q^{64} - 480 q^{66} + 568 q^{71} - 256 q^{74} - 176 q^{79} - 320 q^{81} - 152 q^{84} + 256 q^{86} + 924 q^{89} + 1252 q^{91} + 720 q^{94} + 96 q^{96} - 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
350.3.i.a 350.i 35.i $8$ $9.537$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}^{5}q^{2}+(\zeta_{24}-2\zeta_{24}^{3}-2\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
350.3.i.b 350.i 35.i $16$ $9.537$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{4}+\beta _{11})q^{2}+(-\beta _{6}+\beta _{12})q^{3}+\cdots\)
350.3.i.c 350.i 35.i $24$ $9.537$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)