Properties

Label 363.4.d
Level $363$
Weight $4$
Character orbit 363.d
Rep. character $\chi_{363}(362,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $5$
Sturm bound $176$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 363.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(176\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(363, [\chi])\).

Total New Old
Modular forms 144 116 28
Cusp forms 120 100 20
Eisenstein series 24 16 8

Trace form

\( 100 q + 4 q^{3} + 372 q^{4} + 36 q^{9} + O(q^{10}) \) \( 100 q + 4 q^{3} + 372 q^{4} + 36 q^{9} + 102 q^{12} - 32 q^{15} + 1420 q^{16} - 2068 q^{25} - 608 q^{27} - 104 q^{31} - 908 q^{34} + 1382 q^{36} - 140 q^{37} + 220 q^{42} + 1542 q^{45} + 1494 q^{48} - 1044 q^{49} - 2844 q^{58} - 3612 q^{60} + 5136 q^{64} - 2140 q^{67} + 2760 q^{69} - 5356 q^{70} - 3666 q^{75} + 1372 q^{78} + 5732 q^{81} + 5808 q^{82} - 1608 q^{91} - 2336 q^{93} + 3100 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(363, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
363.4.d.a 363.d 33.d $4$ $21.418$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}-8q^{4}+(-2\beta _{2}+\beta _{3})q^{7}+\cdots\)
363.4.d.b 363.d 33.d $4$ $21.418$ \(\Q(\sqrt{-2}, \sqrt{13})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(1-\beta _{1})q^{3}+5q^{4}+4\beta _{1}q^{5}+\cdots\)
363.4.d.c 363.d 33.d $12$ $21.418$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}-\beta _{1}q^{3}+(8-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
363.4.d.d 363.d 33.d $40$ $21.418$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
363.4.d.e 363.d 33.d $40$ $21.418$ None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(363, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(363, [\chi]) \cong \)