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Properties

Label 775.3.d
Level $775$
Weight $3$
Character orbit 775.d
Rep. character $\chi_{775}(526,\cdot)$
Character field $\Q$
Dimension $99$
Newform subspaces $10$
Sturm bound $240$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 775.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(240\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(775, [\chi])\).

Total New Old
Modular forms 166 105 61
Cusp forms 154 99 55
Eisenstein series 12 6 6

Trace form

\( 99 q + 2 q^{2} + 202 q^{4} + 4 q^{7} - 5 q^{8} - 293 q^{9} + O(q^{10}) \) \( 99 q + 2 q^{2} + 202 q^{4} + 4 q^{7} - 5 q^{8} - 293 q^{9} - 23 q^{14} + 350 q^{16} + 18 q^{18} - 36 q^{19} + 69 q^{28} + 19 q^{31} + 122 q^{32} + 32 q^{33} - 838 q^{36} - 175 q^{38} - 48 q^{39} + 56 q^{41} + 82 q^{47} + 399 q^{49} - 132 q^{51} - 280 q^{56} + 284 q^{59} - 130 q^{62} + 56 q^{63} + 471 q^{64} + 122 q^{67} - 296 q^{69} + 188 q^{71} + 367 q^{72} - 75 q^{76} - 500 q^{78} + 695 q^{81} + 109 q^{82} - 144 q^{87} + 68 q^{93} - 192 q^{94} - 392 q^{97} + 855 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(775, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
775.3.d.a 775.d 31.b $2$ $21.117$ \(\Q(\sqrt{-31}) \) \(\Q(\sqrt{-155}) \) 155.3.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{3}-4q^{4}-22q^{9}+4\beta q^{12}+4\beta q^{13}+\cdots\)
775.3.d.b 775.d 31.b $2$ $21.117$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-155}) \) 155.3.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}-4q^{4}+4q^{9}-4\beta q^{12}-6\beta q^{13}+\cdots\)
775.3.d.c 775.d 31.b $2$ $21.117$ \(\Q(\sqrt{-26}) \) None 31.3.b.a \(2\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta q^{3}-3q^{4}-\beta q^{6}-8q^{7}+\cdots\)
775.3.d.d 775.d 31.b $3$ $21.117$ 3.3.837.1 \(\Q(\sqrt{-31}) \) 31.3.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+(4+\beta _{1}-2\beta _{2})q^{4}+(-5\beta _{1}+\cdots)q^{7}+\cdots\)
775.3.d.e 775.d 31.b $4$ $21.117$ 4.0.8000.2 None 155.3.d.a \(4\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{1}q^{3}-3q^{4}+\beta _{1}q^{6}+(6-\beta _{3})q^{7}+\cdots\)
775.3.d.f 775.d 31.b $6$ $21.117$ 6.6.1389928896.1 \(\Q(\sqrt{-31}) \) 155.3.c.c \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{2}+(4-\beta _{2})q^{4}-\beta _{4}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
775.3.d.g 775.d 31.b $16$ $21.117$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 155.3.d.b \(-4\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{2}-\beta _{1}q^{3}+(3-\beta _{6})q^{4}+\beta _{13}q^{6}+\cdots\)
775.3.d.h 775.d 31.b $20$ $21.117$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 155.3.c.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2+\beta _{4})q^{4}+\beta _{7}q^{6}+\cdots\)
775.3.d.i 775.d 31.b $22$ $21.117$ None 775.3.d.i \(0\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{2}]$
775.3.d.j 775.d 31.b $22$ $21.117$ None 775.3.d.i \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(775, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(775, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)