Properties

Label 350.3.b
Level $350$
Weight $3$
Character orbit 350.b
Rep. character $\chi_{350}(251,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $4$
Sturm bound $180$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 350.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(180\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(23\)

Dimensions

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

Total New Old
Modular forms 132 24 108
Cusp forms 108 24 84
Eisenstein series 24 0 24

Trace form

\( 24 q + 48 q^{4} + 4 q^{7} - 48 q^{9} + O(q^{10}) \) \( 24 q + 48 q^{4} + 4 q^{7} - 48 q^{9} + 8 q^{14} + 96 q^{16} - 32 q^{18} + 8 q^{21} + 48 q^{22} + 72 q^{23} + 8 q^{28} - 64 q^{29} - 96 q^{36} - 136 q^{37} - 312 q^{39} - 80 q^{42} - 128 q^{43} + 32 q^{46} + 72 q^{49} - 296 q^{51} + 208 q^{53} + 16 q^{56} + 24 q^{57} + 224 q^{58} - 380 q^{63} + 192 q^{64} + 112 q^{67} + 312 q^{71} - 64 q^{72} + 256 q^{74} + 408 q^{77} - 320 q^{78} - 96 q^{79} - 88 q^{81} + 16 q^{84} - 160 q^{86} + 96 q^{88} + 208 q^{91} + 144 q^{92} + 824 q^{93} - 48 q^{98} + 392 q^{99} + O(q^{100}) \)

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.b.a 350.b 7.b $4$ $9.537$ 4.0.7168.1 None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{6}+\cdots\)
350.3.b.b 350.b 7.b $4$ $9.537$ 4.0.7168.1 None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots\)
350.3.b.c 350.b 7.b $8$ $9.537$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{5}q^{3}+2q^{4}+(-\beta _{4}+\beta _{7})q^{6}+\cdots\)
350.3.b.d 350.b 7.b $8$ $9.537$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-\beta _{1}q^{3}+2q^{4}-\beta _{4}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)