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Properties

Label 1428.2.d
Level $1428$
Weight $2$
Character orbit 1428.d
Rep. character $\chi_{1428}(169,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $3$
Sturm bound $576$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1428.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(576\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1428, [\chi])\).

Total New Old
Modular forms 300 20 280
Cusp forms 276 20 256
Eisenstein series 24 0 24

Trace form

\( 20 q - 20 q^{9} + O(q^{10}) \) \( 20 q - 20 q^{9} - 20 q^{13} + 4 q^{15} + 4 q^{17} - 4 q^{19} + 4 q^{21} - 24 q^{25} + 4 q^{33} - 4 q^{43} - 8 q^{47} - 20 q^{49} - 8 q^{51} + 4 q^{55} + 24 q^{59} + 32 q^{67} - 4 q^{69} - 16 q^{77} + 20 q^{81} - 32 q^{83} + 28 q^{85} - 40 q^{89} - 16 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1428, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1428.2.d.a 1428.d 17.b $2$ $11.403$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-iq^{7}-q^{9}+4iq^{11}-2q^{13}+\cdots\)
1428.2.d.b 1428.d 17.b $6$ $11.403$ 6.0.38738176.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{4}q^{5}-\beta _{1}q^{7}-q^{9}+(-3\beta _{1}+\cdots)q^{11}+\cdots\)
1428.2.d.c 1428.d 17.b $12$ $11.403$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{3}+\beta _{1}q^{5}-\beta _{8}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1428, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 6}\)