Properties

Label 294.7.b
Level $294$
Weight $7$
Character orbit 294.b
Rep. character $\chi_{294}(197,\cdot)$
Character field $\Q$
Dimension $82$
Newform subspaces $6$
Sturm bound $392$
Trace bound $6$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 294.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(392\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(294, [\chi])\).

Total New Old
Modular forms 352 82 270
Cusp forms 320 82 238
Eisenstein series 32 0 32

Trace form

\( 82 q + 42 q^{3} - 2624 q^{4} + 32 q^{6} - 126 q^{9} + O(q^{10}) \) \( 82 q + 42 q^{3} - 2624 q^{4} + 32 q^{6} - 126 q^{9} + 576 q^{10} - 1344 q^{12} + 4460 q^{13} - 2416 q^{15} + 83968 q^{16} + 704 q^{18} + 884 q^{19} - 14784 q^{22} - 1024 q^{24} - 271286 q^{25} + 90594 q^{27} - 93984 q^{30} + 19532 q^{31} - 63808 q^{33} - 97728 q^{34} + 4032 q^{36} + 43772 q^{37} + 137308 q^{39} - 18432 q^{40} + 445220 q^{43} + 5768 q^{45} - 201216 q^{46} + 43008 q^{48} - 528104 q^{51} - 142720 q^{52} - 22432 q^{54} - 896208 q^{55} + 484884 q^{57} + 511872 q^{58} + 77312 q^{60} + 271292 q^{61} - 2686976 q^{64} - 70336 q^{66} - 1683676 q^{67} + 573080 q^{69} - 22528 q^{72} + 1660196 q^{73} - 1031534 q^{75} - 28288 q^{76} + 914432 q^{78} + 1888892 q^{79} + 555466 q^{81} + 408768 q^{82} - 5101296 q^{85} - 3463160 q^{87} + 473088 q^{88} + 80960 q^{90} - 126364 q^{93} + 3393216 q^{94} + 32768 q^{96} + 2256308 q^{97} + 2392208 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(294, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
294.7.b.a 294.b 3.b $2$ $67.636$ \(\Q(\sqrt{-2}) \) None \(0\) \(-42\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-21-3\beta )q^{3}-2^{5}q^{4}+30\beta q^{5}+\cdots\)
294.7.b.b 294.b 3.b $12$ $67.636$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}-2^{5}q^{4}+(\beta _{2}+\beta _{11})q^{5}+\cdots\)
294.7.b.c 294.b 3.b $12$ $67.636$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(84\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(7+\beta _{2})q^{3}-2^{5}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
294.7.b.d 294.b 3.b $16$ $67.636$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-2^{5}q^{4}+(\beta _{2}-\beta _{5}+\cdots)q^{5}+\cdots\)
294.7.b.e 294.b 3.b $16$ $67.636$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}-2^{5}q^{4}+(-\beta _{1}+\beta _{9}+\cdots)q^{5}+\cdots\)
294.7.b.f 294.b 3.b $24$ $67.636$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{7}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)