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Properties

Label 350.5.d
Level $350$
Weight $5$
Character orbit 350.d
Rep. character $\chi_{350}(349,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $3$
Sturm bound $300$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 350.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(300\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(350, [\chi])\).

Total New Old
Modular forms 252 48 204
Cusp forms 228 48 180
Eisenstein series 24 0 24

Trace form

\( 48 q - 384 q^{4} + 1224 q^{9} + O(q^{10}) \) \( 48 q - 384 q^{4} + 1224 q^{9} - 480 q^{11} - 384 q^{14} + 3072 q^{16} + 1016 q^{21} + 192 q^{29} - 9792 q^{36} + 14376 q^{39} + 3840 q^{44} - 9856 q^{46} - 13456 q^{49} + 17848 q^{51} + 3072 q^{56} - 24576 q^{64} - 23736 q^{71} - 25728 q^{74} + 21088 q^{79} + 5024 q^{81} - 8128 q^{84} + 11520 q^{86} + 14536 q^{91} - 80376 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
350.5.d.a 350.d 35.c $8$ $36.179$ 8.0.\(\cdots\).26 None 14.5.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-\beta _{4}q^{3}-8q^{4}-\beta _{6}q^{6}+(19\beta _{1}+\cdots)q^{7}+\cdots\)
350.5.d.b 350.d 35.c $16$ $36.179$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 70.5.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{11}q^{2}-\beta _{5}q^{3}-8q^{4}+(\beta _{7}+3\beta _{10}+\cdots)q^{6}+\cdots\)
350.5.d.c 350.d 35.c $24$ $36.179$ None 350.5.b.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(350, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)