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Properties

Label 175.5.m
Level $175$
Weight $5$
Character orbit 175.m
Rep. character $\chi_{175}(34,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $312$
Sturm bound $100$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 175.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(100\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(175, [\chi])\).

Total New Old
Modular forms 328 328 0
Cusp forms 312 312 0
Eisenstein series 16 16 0

Trace form

\( 312 q - 10 q^{2} + 602 q^{4} + 440 q^{8} - 2004 q^{9} + O(q^{10}) \) \( 312 q - 10 q^{2} + 602 q^{4} + 440 q^{8} - 2004 q^{9} + 84 q^{11} + 135 q^{14} - 360 q^{15} - 4678 q^{16} - 756 q^{21} + 1590 q^{22} + 5240 q^{23} - 2460 q^{25} + 6075 q^{28} - 996 q^{29} - 11830 q^{30} - 4925 q^{35} + 23176 q^{36} - 10 q^{37} - 2342 q^{39} - 13685 q^{42} + 2874 q^{44} + 12370 q^{46} + 3402 q^{49} - 19060 q^{50} + 788 q^{51} + 16040 q^{53} + 2010 q^{56} - 6910 q^{58} + 5140 q^{60} + 3250 q^{63} + 72432 q^{64} + 23880 q^{65} + 7190 q^{67} - 14270 q^{70} - 27096 q^{71} - 57390 q^{72} - 19460 q^{74} - 5400 q^{77} + 800 q^{78} - 14546 q^{79} - 640 q^{81} - 26986 q^{84} - 10630 q^{85} + 1470 q^{86} + 53540 q^{88} - 10066 q^{91} + 11240 q^{92} + 7340 q^{95} - 15235 q^{98} + 32292 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.