Properties

Label 294.5.c
Level $294$
Weight $5$
Character orbit 294.c
Rep. character $\chi_{294}(97,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $4$
Sturm bound $280$
Trace bound $22$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 294.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(280\)
Trace bound: \(22\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(294, [\chi])\).

Total New Old
Modular forms 240 28 212
Cusp forms 208 28 180
Eisenstein series 32 0 32

Trace form

\( 28 q + 224 q^{4} - 756 q^{9} + O(q^{10}) \) \( 28 q + 224 q^{4} - 756 q^{9} + 408 q^{11} + 144 q^{15} + 1792 q^{16} - 1664 q^{22} + 240 q^{23} - 5484 q^{25} + 3168 q^{29} + 1152 q^{30} - 6048 q^{36} - 2444 q^{37} - 3060 q^{39} - 10172 q^{43} + 3264 q^{44} + 1920 q^{46} + 9216 q^{50} - 1296 q^{51} + 6432 q^{53} - 180 q^{57} - 14528 q^{58} + 1152 q^{60} + 14336 q^{64} + 11352 q^{65} + 25852 q^{67} + 23304 q^{71} - 29184 q^{74} - 10368 q^{78} + 32196 q^{79} + 20412 q^{81} - 26880 q^{85} - 21120 q^{86} - 13312 q^{88} + 1920 q^{92} - 16236 q^{93} - 36456 q^{95} - 11016 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(294, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
294.5.c.a 294.c 7.b $4$ $30.391$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{3}+8q^{4}+(-11\beta _{2}+\cdots)q^{5}+\cdots\)
294.5.c.b 294.c 7.b $8$ $30.391$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{1}q^{2}-3\beta _{2}q^{3}+8q^{4}+(5\beta _{4}-11\beta _{5}+\cdots)q^{5}+\cdots\)
294.5.c.c 294.c 7.b $8$ $30.391$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{1}q^{2}+\beta _{4}q^{3}+8q^{4}+(-5\beta _{2}+\cdots)q^{5}+\cdots\)
294.5.c.d 294.c 7.b $8$ $30.391$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-3\beta _{1}q^{3}+8q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)