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Properties

Label 2040.2.m
Level $2040$
Weight $2$
Character orbit 2040.m
Rep. character $\chi_{2040}(409,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $10$
Sturm bound $864$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 2040 = 2^{3} \cdot 3 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2040.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(864\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2040, [\chi])\).

Total New Old
Modular forms 448 48 400
Cusp forms 416 48 368
Eisenstein series 32 0 32

Trace form

\( 48 q - 48 q^{9} - 8 q^{11} - 4 q^{15} + 8 q^{19} - 12 q^{25} + 8 q^{31} + 8 q^{35} + 24 q^{41} - 48 q^{49} - 12 q^{51} - 4 q^{55} - 8 q^{59} + 24 q^{61} - 24 q^{65} + 32 q^{71} - 56 q^{79} + 48 q^{81} - 16 q^{89}+ \cdots + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(2040, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2040.2.m.a 2040.m 5.b $2$ $16.289$ \(\Q(\sqrt{-1}) \) None 2040.2.m.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{3}+(i-2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
2040.2.m.b 2040.m 5.b $2$ $16.289$ \(\Q(\sqrt{-1}) \) None 2040.2.m.b \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{3}+(-i-2)q^{5}+4 i q^{7}-q^{9}+\cdots\)
2040.2.m.c 2040.m 5.b $2$ $16.289$ \(\Q(\sqrt{-1}) \) None 2040.2.m.c \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{3}+(-2 i-1)q^{5}+i q^{7}-q^{9}+\cdots\)
2040.2.m.d 2040.m 5.b $2$ $16.289$ \(\Q(\sqrt{-1}) \) None 2040.2.m.d \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{3}+(-2 i-1)q^{5}+3 i q^{7}+\cdots\)
2040.2.m.e 2040.m 5.b $2$ $16.289$ \(\Q(\sqrt{-1}) \) None 2040.2.m.e \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{3}+(-2 i+1)q^{5}+5 i q^{7}+\cdots\)
2040.2.m.f 2040.m 5.b $2$ $16.289$ \(\Q(\sqrt{-1}) \) None 2040.2.m.f \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{3}+(i+2)q^{5}-q^{9}+2 q^{11}+\cdots\)
2040.2.m.g 2040.m 5.b $2$ $16.289$ \(\Q(\sqrt{-1}) \) None 2040.2.m.g \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{3}+(i+2)q^{5}+4 i q^{7}-q^{9}+\cdots\)
2040.2.m.h 2040.m 5.b $10$ $16.289$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 2040.2.m.h \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}-\beta _{6}q^{5}+(\beta _{4}+\beta _{5})q^{7}-q^{9}+\cdots\)
2040.2.m.i 2040.m 5.b $12$ $16.289$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 2040.2.m.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}-\beta _{9}q^{5}-\beta _{7}q^{7}-q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2040.2.m.j 2040.m 5.b $12$ $16.289$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 2040.2.m.j \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}-\beta _{2}q^{5}+(-\beta _{6}+\beta _{7}-\beta _{8}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2040, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2040, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(680, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1020, [\chi])\)\(^{\oplus 2}\)