Properties

Label 1596.2.i
Level $1596$
Weight $2$
Character orbit 1596.i
Rep. character $\chi_{1596}(265,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $2$
Sturm bound $640$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1596.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(640\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1596, [\chi])\).

Total New Old
Modular forms 332 28 304
Cusp forms 308 28 280
Eisenstein series 24 0 24

Trace form

\( 28 q - 2 q^{7} + 28 q^{9} + 12 q^{11} - 16 q^{25} + 2 q^{35} - 16 q^{39} - 44 q^{43} + 30 q^{49} - 2 q^{63} - 14 q^{77} + 28 q^{81} - 20 q^{85} - 32 q^{93} - 28 q^{95} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(1596, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1596.2.i.a 1596.i 133.c $14$ $12.744$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 1596.2.i.a \(0\) \(-14\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{10}q^{5}+\beta _{11}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
1596.2.i.b 1596.i 133.c $14$ $12.744$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 1596.2.i.a \(0\) \(14\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\beta _{10}q^{5}+\beta _{11}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1596, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1596, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(532, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)