Properties

Label 2394.2.b
Level $2394$
Weight $2$
Character orbit 2394.b
Rep. character $\chi_{2394}(1709,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $10$
Sturm bound $960$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2394.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(960\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(29\), \(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2394, [\chi])\).

Total New Old
Modular forms 496 40 456
Cusp forms 464 40 424
Eisenstein series 32 0 32

Trace form

\( 40 q + 40 q^{4} + O(q^{10}) \) \( 40 q + 40 q^{4} + 40 q^{16} + 16 q^{19} - 56 q^{25} - 32 q^{43} + 40 q^{49} + 16 q^{58} + 80 q^{61} + 40 q^{64} + 16 q^{73} + 16 q^{76} + 16 q^{82} + 96 q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2394, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2394.2.b.a 2394.b 57.d $2$ $19.116$ \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-\beta q^{13}+q^{14}+\cdots\)
2394.2.b.b 2394.b 57.d $2$ $19.116$ \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+2\beta q^{5}+q^{7}-q^{8}-2\beta q^{10}+\cdots\)
2394.2.b.c 2394.b 57.d $2$ $19.116$ \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
2394.2.b.d 2394.b 57.d $2$ $19.116$ \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-\beta q^{13}-q^{14}+\cdots\)
2394.2.b.e 2394.b 57.d $2$ $19.116$ \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+2\beta q^{5}+q^{7}+q^{8}+2\beta q^{10}+\cdots\)
2394.2.b.f 2394.b 57.d $2$ $19.116$ \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
2394.2.b.g 2394.b 57.d $6$ $19.116$ 6.0.2803712.1 None \(-6\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}-q^{8}+\beta _{1}q^{10}+\cdots\)
2394.2.b.h 2394.b 57.d $6$ $19.116$ 6.0.2803712.1 None \(6\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}+q^{8}-\beta _{1}q^{10}+\cdots\)
2394.2.b.i 2394.b 57.d $8$ $19.116$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-8\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+\beta _{3}q^{5}-q^{7}-q^{8}-\beta _{3}q^{10}+\cdots\)
2394.2.b.j 2394.b 57.d $8$ $19.116$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(8\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+\beta _{3}q^{5}-q^{7}+q^{8}+\beta _{3}q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2394, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)