Properties

Label 1805.2.b
Level $1805$
Weight $2$
Character orbit 1805.b
Rep. character $\chi_{1805}(1084,\cdot)$
Character field $\Q$
Dimension $154$
Newform subspaces $13$
Sturm bound $380$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(380\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1805, [\chi])\).

Total New Old
Modular forms 210 188 22
Cusp forms 170 154 16
Eisenstein series 40 34 6

Trace form

\( 154 q - 138 q^{4} + 4 q^{5} - 118 q^{9} + O(q^{10}) \) \( 154 q - 138 q^{4} + 4 q^{5} - 118 q^{9} - 8 q^{10} + 4 q^{11} + 12 q^{14} - 10 q^{15} + 114 q^{16} - 30 q^{20} - 20 q^{21} + 4 q^{25} - 4 q^{26} + 24 q^{29} - 24 q^{30} + 8 q^{31} - 16 q^{34} - 8 q^{35} + 106 q^{36} - 44 q^{39} + 4 q^{40} + 8 q^{41} + 28 q^{44} + 16 q^{45} - 4 q^{46} - 54 q^{49} - 4 q^{50} - 4 q^{51} - 24 q^{54} + 16 q^{55} - 52 q^{56} + 20 q^{59} - 20 q^{60} + 8 q^{61} - 34 q^{64} + 12 q^{65} + 164 q^{66} - 24 q^{69} - 16 q^{70} - 60 q^{71} - 20 q^{74} + 34 q^{75} - 16 q^{79} + 76 q^{80} - 38 q^{81} - 24 q^{84} - 24 q^{85} + 20 q^{86} + 20 q^{89} + 40 q^{90} + 32 q^{91} - 36 q^{94} + 52 q^{96} - 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1805, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1805.2.b.a 1805.b 5.b $2$ $14.413$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2q^{4}+(-1+i)q^{5}+2iq^{7}+\cdots\)
1805.2.b.b 1805.b 5.b $2$ $14.413$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2q^{4}+(-1-i)q^{5}-2iq^{7}+\cdots\)
1805.2.b.c 1805.b 5.b $2$ $14.413$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+(-1-2i)q^{5}+2iq^{7}+\cdots\)
1805.2.b.d 1805.b 5.b $2$ $14.413$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-1\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}+(-1+\beta )q^{5}+(-1+2\beta )q^{7}+\cdots\)
1805.2.b.e 1805.b 5.b $6$ $14.413$ 6.0.16516096.1 None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
1805.2.b.f 1805.b 5.b $6$ $14.413$ 6.0.4227136.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
1805.2.b.g 1805.b 5.b $6$ $14.413$ 6.0.4227136.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
1805.2.b.h 1805.b 5.b $8$ $14.413$ 8.0.\(\cdots\).2 \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
1805.2.b.i 1805.b 5.b $16$ $14.413$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
1805.2.b.j 1805.b 5.b $16$ $14.413$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
1805.2.b.k 1805.b 5.b $24$ $14.413$ None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1805.2.b.l 1805.b 5.b $24$ $14.413$ None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1805.2.b.m 1805.b 5.b $40$ $14.413$ None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1805, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)